ὁ κηρύσσων μὴ κλέπτειν κλέπτεις;
He who preaches to not steal, do you steal?
ὁ λέγων μὴ μοιχεύειν μοιχεύεις;
He who says to not commit adultery, do you commit adultery?
ὁ βδελυσσόμενος τὰ εἴδωλα ἱεροσυλεῖς;
He who abhors idols, do you [X]?
As you mentioned, there is a clear opposition between the former clause and the latter clause in each verse. The individual who preaches against a certain act hypocritically commits the same or similar act.
ἱεροσυλεῖς is conjugated from the verb ἱεροσυλέω in the 2nd person, singular number, present tense, active voice, and indicative mood.
BDAG (p. 471) defines ἱεροσυλέω as follows:
ἱεροσυλέω (s. ἱερός, συλάω, and next entry; on the terminal formation s. DELG s.v. συλάω; Aristoph. et al.; Polyb. 30, 26, 9; Artem. 3, 3; Heraclitus, Ep. 7, 4H.; SIG 417, 8; 10 [273/272 B.C.; cp. ἱεροσυλία 1017, 18; in tales of Alexander: PSI II, 1285 col. I, 38; col. III, 42; col. IV, 9 [II A.D.]; 2 Macc 13:6; ἱεροσύλημα 4:39; ἱερόσυλος 4:42]; 2 Macc 9:2; Philo; Jos., C. Ap. 1, 249, Ant. 17, 163)
to take objects from a temple by force or stealth, rob temples (Manetho: 609 Fgm. 10a, 249 Jac. [=Jos., C. Ap. 1, 249], w. vandalism against sacred images) prob. to be taken literally of temple plundering Ro 2:22 (w. κλέπτω and μοιχεύω as Philo, Conf. Lingu. 163; cp. also Herm. Wr. 12, 5; JDerrett, NTS 40, ’94, 558–71 w. focus on violation of conscience). Some interpret ἱ. in this pass. as meaning
to commit irreverent acts, commit sacrilege (in Isaeus 8, 39 ἱεροσυλία is used of conduct relating to burial rites).—EKrentz, The Name of God in Disrepute—Romans 2:17–29: CTM 17, ’90, 429–39.—DELG s.v. συλάω. M-M. TW.
LSJ (p. 822) defines ἱεροσυλέω as follows:
ἱεροσῡλέω, pf. ἱεροσύληκα SIG417.8 (Delph., iii B.C.):—rob a temple, commit sacrilege, Ar.V.845, Antipho 5.10, Pl.R.575b.
II. c. acc., ἱ. τὰ ὅπλα steal the sacred arms, D.57.64, cf. Lycurg.136; ἱ. τὰ ἱερά rob or plunder the temples, Plb.30.26.9; θεούς Phalar.Ep.84.1.
Thayer (pp. 299-300) defines ἱεροσυλέω as follows:
ἱερο-συλέω, -ῶ; (ἱερόσυλος, q. v.); to commit sacrilege, to rob a temple: Ro. 2:22, where the meaning is, ‘thou who abhorrest idols and their contamination, dost yet not hesitate to plunder their shrines’; cf. Fritzsche [and Delitzsch] ad loc. (Arstph., Plat., Dem., al.)*
While ἱεροσυλέω is a hapax legomenon, the related noun ἱερόσυλος also occurs in Acts 19:37.
There was a "silversmith" (ἀργυροκόπος) named Demetrius, and he made "silver temples" (ναοὶ ἀργύρεοι)(1) for the goddess Artemis (Ἄρτεμις) (Acts 19:24). By that business, he and other such silversmiths made their "wealth" (εὐπορία) (Acts 19:25). Therefore, the silver temples were very costly, and Demetrius and his fellows opposed any effort that would have deprived him of his income received from making the silver temples (Acts 19:27). After an uproar, a crowd of people take Paul's companions Gaius and Aristarchus into the public theater, where eventually the townclerk of the city declares,
For you have brought these men who are neither [ἱεροσύλους] nor blasphemers of your goddess.
ἠγάγετε γὰρ τοὺς ἄνδρας τούτους οὔτε ἱεροσύλους οὔτε βλασφημοῦντας τὴν θεὰν ὑμῶν
So, the people accused Paul's companions of blaspheming Artemis, but what does ἱεροσύλους mean? Well, the meaning of the word is literally "temple robber." It's possible that his companions were accused of robbing the great temple of Artemis in Ephesus, but the other alternative is they were accused of robbing the silver temples or idols of Artemis. Why rob them? Simple. They were expensive and thus a great source of εὐπορία.
The Meaning in Romans 2:22
Returning to Rom. 2:22,
ὁ βδελυσσόμενος τὰ εἴδωλα ἱεροσυλεῖς;
He who abhors idols, do you [X]?
There simply seems to be no reason why we shouldn't translate it according to the word's simple meaning.
He who abhors idols, do you rob temples?
Of course, the reason for robbing temples was to sell the costly idols therein, often made of silver or gold. But, the hypocrisy lies in the fact that one acts righteous by hating idols, yet he sins by stealing the same idols to sell them.
Consider Josephus' statement in his Jewish Antiquities:(2)
Let no one blaspheme those gods which other cities esteem such; nor may anyone steal what belongs to strange temples; nor take away the gifts that are dedicated to any god.
Βλασφημείτω δὲ μηδεὶς θεοὺς οὓς πόλεις ἄλλαι νομίζουσι. μηδὲ συλᾶν ἱερὰ ξενικά, μηδ ̓ ἂν ἐπωνομασμένον ᾖ τινι θεῷ κειμήλιον λαμβάνειν.
Whiston translated συλᾶν ἱερὰ ξενικά as "steal what belongs to strange temples," but it's simply "rob strange temples." Thus, robbing temples (for the costly items therein) was apparently something that occurred during that era.
Footnotes
(1) In his commentary on Acts 19:24, St. Chrysostom writes,
And how were they made into silver temples? Perhaps as small boxes.
Καὶ πῶς ἔνι ναοὺς ἀργυροῦς γενέσθαι; Ἴσως ὡς κιβώρια μικρά·
(2) Jewish Antiquities, 4.8.10 (4.207)
References
Bauer, Walter; Danker, Frederick William. A Greek-English Lexicon of the New Testament and Other Early Christian Literature. 3rd ed. Chicago: University of Chicago Press, 2000.
Josephus; Whiston, William. The Works of Josephus: Complete and Unabridged. Peabody: Hendrickson, 1987.
Liddell, Henry George; Scott, Robert. A Greek-English Lexicon. 9th ed. with supplement. Oxford: Clarendon Press, 1996.
Thayer, Joseph Henry. A Greek-English Lexicon of the New Testament. New York: American Book, 1889.