The word ἐκκλησία used in the LXX of Deuteronomy 23 is not a "reserved word" that always refers to the body of Christ. BDAG lists many usages:
ἐκκλησία, ας, ἡ (ἐκ + καλέω; Eur., Hdt.+)
① a regularly summoned legislative body, assembly, as gener. understood in the Gr-Rom. world (Jos., Ant. 12, 164; 19, 332, Vi. 268) Ac 19:39 (on ‘[regular] statutory assembly’, s. ἔννομος and IBM III/2, p. 141. The term ἐννόμη ἐ. here contrasts w. the usage vss. 32 and 40, in which ἐ. denotes simply ‘a gathering’; s. 2 below. On the ἐ. in Ephesus cp. CIG III, 325; IBM III/1, 481, 340; on the ἐ. in the theater there s. the last-named ins ln. 395; OGI 480, 9).—Pauly-W. V/2, 1905, 2163–2200; RAC IV 905–21 (lit.).
② a casual gathering of people, an assemblage, gathering (cp. 1 Km 19:20; 1 Macc 3:13; Sir 26:5) Ac 19:32, 40.
③ people with shared belief, community, congregation (for common identity, cp. the community of Pythagoras [Hermippus in Diog. L. 8, 41]. Remarkably, in Himerius, Or. 39 [Or. 5], 5 Orpheus forms for himself τὴν ἐκκλησίαν, a group of wild animals, who listen to him, in the Thracian mountains where there are no people), in our lit. of common interest in the God of Israel.
ⓐ of OT Israelites assembly, congregation (Dt 31:30; Judg 20:2; 1 Km 17:47; 3 Km 8:14; PsSol 10:6; TestJob 32:8 τῆς εὐώδους ἐ.; Philo; Jos., Ant. 4, 309; Diod S 40, 3, 6) Hb 2:12 (Ps 21:23); e.g. to hear the law (Dt 4:10; 9:10; 18:16) Ac 7:38.
ⓑ of Christians in a specific place or area (the term ἐ. apparently became popular among Christians in Greek-speaking areas for chiefly two reasons: to affirm continuity with Israel through use of a term found in Gk. translations of the Hebrew Scriptures, and to allay any suspicion, esp. in political circles, that Christians were a disorderly group).
α. of a specific Christian group assembly, gathering ordinarily involving worship and discussion of matters of concern to the community: Mt 18:17; συνερχομένων ὑμῶν ἐν ἐ. when you come together as an assembly 1 Cor 11:18; cp. 14:4f, 12, 19, 28, p 304 35; pl. vs. 34. ἐν ἐ. ἐξομολογεῖσθαι τὰ παραπτώματα confess one’s sins in assembly D 4:14; cp. 3J 6 (JCampbell, JTS 49, ’48, 130–42; for the Johannines s. ESchweizer below). In Ac 15:22 the ‘apostles and elders’ function in the manner of the βουλή or council, the committee of the whole that was responsible in a Gr-Rom. polis for proposing legislation to the assembly of citizens.—Of Christians gathering in the home of a patron house-assembly (‘house-church’) Πρίσκαν καὶ Ἀκύλαν … καὶ τὴν κατʼ οἶκον αὐτῶν ἐ. Ro 16:5; cp. 1 Cor 16:19. Νύμφαν καὶ τὴν κατʼ οἶκον αὐτῆς ἐ. Col 4:15; ἡ κατʼ οἶκόν σου ἐ. Phlm 2.—FFilson, JBL 58, ’39, 105–12; other reff. οἶκος 1aα.—Pl. ἐ. τῶν ἁγίων 1 Cor 14:33; ἐ. τῶν ἐθνῶν Ro 16:4.—1 Ti 5:16 prob. belongs here, s. βαρέω b.
β. congregation or church as the totality of Christians living and meeting in a particular locality or larger geographical area, but not necessarily limited to one meeting place: Ac 5:11; 8:3; 9:31 (so KGiles, NTS 31, ’85, 135–42; s. c below), 11:26; 12:5; 15:3; 18:22; 20:17; cp. 12:1; 1 Cor 4:17; Phil 4:15; 1 Ti 5:16 perh., s. α above; Js 5:14; 3 J 9f; 1 Cl 44:3; Hv 2, 4, 3. More definitely of the Christians in Jerusalem Ac 8:1; 11:22; cp. 2:47 v.l.; 15:4, 22; Cenchreae Ro 16:1; cp. vs. 23; Corinth 1 Cor 1:2; 2 Cor 1:1; 1 Cl ins; 47:6; AcPlCor 1:16; Laodicea Col 4:16; Rv 3:14; Thessalonica 1 Th 1:1; 2 Th 1:1; Colossae Phlm subscr. v.l. Likew. w. other names: Rv 2:1, 8, 12, 18; 3:1, 7; IEph ins; 8:1; IMg ins; ITr ins; 13:1; IRo 9:1; IPhld ins; 10:1; ISm 11:1; Pol ins. Plural: Ac 15:41; 16:5; Ro 16:16; 1 Cor 7:17; 2 Cor 8:18f, 23f; 11:8, 28; 12:13; Rv 2:7, 11, 17, 23, 29; 3:6, 13, 22; 22:16; the Christian community in Judea Gal 1:22; 1 Th 2:14; Galatia Gal 1:2; 1 Cor 16:1; Asia vs. 19; Rv 1:4, and cp. vss. 11 and 20; Macedonia 2 Cor 8:1. κατʼ ἐκκλησίαν in each individual congregation or assembly Ac 14:23 (on the syntax cp. OGI 480, 9 [s. 1 above]: ἵνα τιθῆνται κατʼ ἐκκλησίαν in order that they [the statues] might be set up at each [meeting of the] ἐ.). On κατὰ τ. οὖσαν ἐ. Ac 13:1 cp. εἰμί 1 end.
ⓒ the global community of Christians, (universal) church (s. AvHarnack, Mission I4 420 n. 2 on Ac 12:1): Mt 16:18 (OBetz, ZNW 48, ’57, 49–77: Qumran parallels; s. HBraun, Qumran I, ’66, 30–37); Ac 9:31 (but s. 3bβ); 1 Cor 6:4; 12:28; Eph 1:22; 3:10, 21; 5:23ff, 27, 29, 32 (HSchlier, Christus u. d. Kirche im Eph 1930; also ThBl 6, 1927, 12–17); Col 1:18, 24; Phil 3:6; B 7:11; Hv 2, 2, 6; 2, 4, 1 (with the depiction of the church as an elderly lady cp. Ps.-Demetr. 265 where Hellas, the homeland, is represented as λαβοῦσα γυναικὸς σχῆμα); 3, 3, 3; IEph 5:1f and oft.—The local assembly or congregation as well as the universal church is more specif. called ἐ. τοῦ θεοῦ or ἐ. τ. Χριστοῦ. This is essentially Pauline usage, and it serves to give the current Gk. term its Christian coloring and thereby its special mng.:
α. ἐ. τοῦ θεοῦ (Orig., C. Cels. 1, 63, 22) 1 Cor 1:2; 10:32; 11:16, 22; 15:9; 2 Cor 1:1; Gal 1:13; 1 Th 2:14; 2 Th 1:4; 1 Ti 3:5, 15; Ac 20:28; ITr 2:3; 12:1; IPhld 10:1; ISm ins al.
β. ἐ. τοῦ Χριστοῦ (Orig., C. Cels. 5, 22, 14) Ro 16:16.
γ. both together ἐ. ἐν θεῷ πατρὶ καὶ κυρίῳ Ἰησοῦ Χριστῷ 1 Th 1:1.
δ. ἡ ἐ. ἡ πρώτη ἡ πνευματική the first, spiritual church (conceived in a Platonic sense as preexistent) 2 Cl 14:1; ἐ. ζῶσα the living church the body of Christ vs. 2; ἡ ἁγία ἐ. Hv 1, 1, 6; 1, 3, 4; ἡ καθολικὴ ἐ. ISm 8:2; ἡ ἁγία καὶ καθολικὴ ἐ. MPol ins; ἡ κατὰ τὴν οἰκουμένην καθολικὴ ἐ. 8:1; 19:2; ἓν σῶμα τῆς ἐ. ISm 1:2.—The literature before ’32 is given in OLinton, D. Problem der Urkirche in d. neueren Forschung (s. esp. 138–46) ’32 and AMedebielle, Dict. de la Bible, Suppl. II ’34, 487–691; before ’60, s. RAC; also s. TW, Sieben, and JHainz, Ekklesia ’72. Esp. important: EBurton, Gal (ICC) 1921, 417–20; KHoll, D. Kirchenbegriff des Pls usw.: SBBerlAk 1921, 920–47=Ges. Aufs. II 1928, 44ff; FKattenbusch, D. Vorzugsstellung d. Petrus u. d. Charakter d. Urgemeinde zu Jerusalem: KMüller Festschr. 1922, 322–51; KLSchmidt, D. Kirche des Urchristentums: Dssm. Festschr. 1927, 259–319, TW III 502–39. S. also: EPeterson, D. Kirche aus Juden u. Heiden ’33; KLSchmidt, D. Polis in Kirche u. Welt ’39; WBieder, Ekkl. u. Polis im NT u. in d. alten Kirche ’41; OMichel, D. Zeugnis des NTs v. d. Gemeinde ’41; NDahl, D. Volk Gottes ’41; RFlew, Jesus and His Church2, ’43; GJohnston, The Doctrine of the Church in the NT ’43; WKümmel, Kirchenbegriff u. Geschichtsbewusstsein in d. Urg. u. b. Jesus ’43; DFaulhaber, D. Johev. u. d. Kirche ’38; AFridrichsen, Kyrkan i 4. ev.: SvTK 16, ’40, 227–42; ESchweizer, NT Essays (Manson memorial vol.) ’59, 230–45; EWolf, Ecclesia Pressa—eccl. militans: TLZ 72, ’47, 223–32; SHanson, Unity of the Church in the NT ’46; HvCampenhausen, Kirchl. Amt u. geistl. Vollmacht in den ersten 3 Jahrh. ’53; EKäsemann, Sätze hlg. Rechtes im NT, NTS 1, ’55, 248–60; AGeorge, ET 58, ’46/47, 312–16; in ATR: JBernardin 21, ’39, 153–70; BEaston 22, ’40, 157–68; SWalke 32, ’50, 39–53 (Apost. Fath.); JMurphy, American Ecclesiastical Review 140, ’59, 250–59; 325–32; PMinear, Images of the Church in the NT, ’60; BMetzger, Theology Today 19, ’62, 369–80; ESchweizer, Church Order in the NT, tr. FClarke ’61; RSchnackenburg, The Church in the NT, tr. WO’Hara ’65; LCerfaux, JBL 85, ’66, 250–51; AHilhorst, Filología Neotestamentaria 1, ’88, 27–34. S. also ἐπίσκοπος 2 end; Πέτρος; πέτρα 1.—B. 1476f. DELG s.v. καλέω. M-M. EDNT. TW. Sv.
Arndt, W., Danker, F. W., Bauer, W., & Gingrich, F. W. (2000). A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed., pp. 303–304). Chicago: University of Chicago Press.
Adam Clarke, I think properly sees the reference in Deuteronomy 23 as not limiting the access of a guy with damaged testicles from being part of Israel but rather being part of the government of Israel:
Deuteronomy 23:1 Shall not enter into the congregation, etc. - If by
entering the congregation be meant the bearing a civil office among
the people, such as magistrate, judge, etc., then the reason of the
law is very plain; no man with any such personal defect as might
render him contemptible in the sight of others should bear rule among
the people, lest the contempt felt for his personal defects might be
transferred to his important office, and thus his authority be
disregarded. The general meaning of these words is, simply, that the
persons here designated should not be so incorporated with the Jews as
to partake of their civil privileges.
- Adam Clarke
So this usage is entirely irrelevant to the question of whether Israel and Paul's "body of Christ" are identical - they are not. Paul claims that he was the architect of that "gathering" or "congregation":
1Co_3:10 According to the grace of God which is given unto me, as a
wise masterbuilder, I have laid the foundation, and another buildeth
thereon. But let every man take heed how he buildeth thereupon.
So Israel and Paul's "body of Christ" are apples and oranges.
However, while on earth Jesus said that he was building an ἐκκλησία:
Matthew 16:18 “And I also say to you that you are Peter, and on this
rock I will build My church, and the gates of Hades shall not prevail
against it. NKJV, 1982
It may be that Jesus was using ἐκκλησία in the sense of a government ala Deuteronomy 23 or of a gathering. Either way, he was not referring to Paul's "body of Christ" (which at that time was an unrevealed mystery) but rather the kingdom of God as prophesied "since the world began":
Act_3:21 Whom the heaven must receive until the times of restitution
of all things, which God hath spoken by the mouth of all his holy
prophets since the world began.
Paul's "body of Christ" however was a mystery never spoken of by the prophets:
Rom_16:25 Now to him that is of power to stablish you according to my
gospel, and the preaching of Jesus Christ, according to the revelation
of the mystery, which was kept secret since the world began,
What Jesus was doing was the Israel-centered reign of messiah from Jerusalem (which though announced in the gospels as "at hand" has been deferred until the future). John, sent to prepare the people was instead murdered and Jesus, the king was likewise. In fact, despite the miraculous signs done by the apostles they too were rebuffed, imprisoned and at least Stephen was slain so that rather than the kingdom arising, Jerusalem and the temple were destroyed:
Mar 12:1 And he began to speak unto them by parables. A certain man
planted a vineyard, and set an hedge about it, and digged a place for
the winefat, and built a tower, and let it out to husbandmen, and went
into a far country. Mar 12:2 And at the season he sent to the
husbandmen a servant, that he might receive from the husbandmen of the
fruit of the vineyard. Mar 12:3 And they caught him, and beat him,
and sent him away empty. Mar 12:4 And again he sent unto them
another servant; and at him they cast stones, and wounded him in the
head, and sent him away shamefully handled. Mar 12:5 And again he
sent another; and him they killed, and many others; beating some, and
killing some. Mar 12:6 Having yet therefore one son, his
wellbeloved, he sent him also last unto them, saying, They will
reverence my son. Mar 12:7 But those husbandmen said among
themselves, This is the heir; come, let us kill him, and the
inheritance shall be ours. Mar 12:8 And they took him, and killed
him, and cast him out of the vineyard. Mar 12:9 What shall therefore
the lord of the vineyard do? he will come and destroy the husbandmen,
and will give the vineyard unto others. Mar 12:10 And have ye not
read this scripture; The stone which the builders rejected is become
the head of the corner: Mar 12:11 This was the Lord's doing, and it
is marvellous in our eyes? Mar 12:12 And they sought to lay hold on
him, but feared the people: for they knew that he had spoken the
parable against them: and they left him, and went their way.
Mat 23:34 Wherefore, behold, I send unto you prophets, and wise men,
and scribes: and some of them ye shall kill and crucify; and some of
them shall ye scourge in your synagogues, and persecute them from city
to city: Mat 23:35 That upon you may come all the righteous blood
shed upon the earth, from the blood of righteous Abel unto the blood
of Zacharias son of Barachias, whom ye slew between the temple and the
altar. Mat 23:36 Verily I say unto you, All these things shall come
upon this generation. Mat 23:37 O Jerusalem, Jerusalem, thou that
killest the prophets, and stonest them which are sent unto thee, how
often would I have gathered thy children together, even as a hen
gathereth her chickens under her wings, and ye would not! Mat 23:38
Behold, your house is left unto you desolate. Mat 23:39 For I say
unto you, Ye shall not see me henceforth, till ye shall say, Blessed
is he that cometh in the name of the Lord.
Paul says that all of this was by divine design so that the body of Christ might come to be:
Rom_11:25 For I would not, brethren, that ye should be ignorant of
this mystery, lest ye should be wise in your own conceits; that
blindness in part is happened to Israel, until the fulness of the
Gentiles be come in. ... Rom 11:30 For as ye in times past have not
believed God, yet have now obtained mercy through their unbelief:
So the relationship of the "body of Christ" to the "Israel program" is not identity (they are not the same thing) they are like the twin sons of Isaac:
Rom 9:6 Not as though the word of God hath taken none effect. For
they are not all Israel, which are of Israel: Rom 9:7 Neither,
because they are the seed of Abraham, are they all children: but, In
Isaac shall thy seed be called. Rom 9:8 That is, They which are the
children of the flesh, these are not the children of God: but the
children of the promise are counted for the seed. Rom 9:9 For this
is the word of promise, At this time will I come, and Sara shall have
a son. Rom 9:10 And not only this; but when Rebecca also had
conceived by one, even by our father Isaac; Rom 9:11 (For the
children being not yet born, neither having done any good or evil,
that the purpose of God according to election might stand, not of
works, but of him that calleth;) Rom 9:12 It was said unto her, The
elder shall serve the younger. Rom 9:13 As it is written, Jacob have
I loved, but Esau have I hated.
In the original scenario the chosen seed was the descendants of Jacob but Paul flips that and makes them Esau and the "body of Christ" are the chosen Jacob! The elder, Israel, is refused, and the "loved" is the body of Christ.
KJV unless otherwise noted.