No, it isn't an accurate translation. At a number of points it strains or simply falsifies the meaning of the Hebrew text. I'll take it phrase by phrase, but first, here's a key for the layout I'll use -- I hope it's clear.
MT: The Masoretic text (Hebrew)
Translit.: and its transliteration
LXX: the Septuagint (ancient Greek translation)
Translit.: and its transliteration
Trans.: and its translation (using the 1851 Lancelot C. L. Brenton version)
GT: The "Gender Tree" translation (OP's question)
TNK: The Tanakh translation
Commentary: my notes
For convenience, in running text, here is the LXX and Tanak:
- LXX The apparel of a man shall not be on a woman, neither shall a man put on a woman’s dress; for every one that does these things is an abomination to the Lord thy God.
- Tanak A woman must not put on man's apparel, nor shall a man wear woman's clothing; for whoever does these things is abhorrent to the LORD your God.
Translit.: lōʾ yihye
LXX: Οὐκ ἔσται
Translit.: ouk estai
Trans.: shall not be
GT: Never cause or force ... to be used
TNK: must not put on
Commentary: The Hebrew is literally "There shall not be", i.e., a negative command or prohibition. The form with "lōʾ" conveys a blanket prohibition, like the Ten Commandments, rather than an immediate or temporary, "don't!" ("Don't touch the stove!"). There is no nuance, hint, or tendency to causation for "forcing" anything or anyone, so this is at least tendentious, and even misleading. The Hebrew is simply a statement of what must never be. The Tanak translation smooths this in English (the context is "apparel") to make it more colloquial, without distorting the meaning. And where "to be used (by)" comes from is anyone's guess. It's not in the Hebrew.
MT: כְלִי־גֶבֶר עַל־אִשָּׁה
Translit.: kĕlî-geber ʿal-ʾiššâ
LXX: σκεύη ἀνδρὸς ἐπὶ γυναικί
Translit.: skeuē andros epi gunaiki
Trans.: The apparel of a man ... on a woman
GT: a warriors weapon ... by a woman or weak person
TNK: A woman ... man's apparel
Commentary: The GT translation indulges in two unwarranted moves here. (1) kĕlî-geber as "a warrior's weapon" is a possible translation, in that the English given provides legitimate glosses on the Hebrew words. However, context determines meaning, and we'll seen in a moment that this (otherwise acceptable) translation is not suitable for the context. The Hebrew word "kĕlî" has a very wide range of meaning, with something like "utensil" as a base meaning. But, as the article linked in the previous sentence demonstrates (see page 3), "clothing" is part of its semantic range, and what we want in context (see below). "geber" is the word GT translates as warrior here: this is just possible, as it usually refers to men who can be part of the fighting force, but even this needs to be explained sometimes (see Jeremiah 41:16 where it spelled out as "gibborim [plural of geber] who were men of war"). In Lamentations 3:1 it is always translated simply "I am the man who has..."
(2) GT's "woman" is fine, but "weak person" is fabrication. It simply isn't there, nor is it an acceptable expansion of Hebrew ʾiššâ which can mean "woman" or "wife", more specifially. It is not a generic term for "weak person".
MT: וְלֹא־יִלְבַּשׁ גֶּבֶר שִׂמְלַת אִשָּׁה
Translit.: wĕlōʾ-yilbaš geber śimlat ʾiššâ
LXX: οὐδὲ μὴ ἐνδύσηται ἀνὴρ στολὴν γυναικείαν
Translit.: oude mē endunasētai anēr stolēn gunaikeian
Trans.: neither shall a man put on a woman’s dress
GT: neither dress warriors armor on a woman or weak person
TNK: nor shall a man wear woman's clothing
Commentary: The errors that GT perpetuates in the preceding phrase are carried forward here. It's hard even to work out how the GT's English can "map" back on to the Hebrew text. The best part about it is the verb "dress", although this is worded so as to imply that there is a dresser, and someone is (passively) being dressed. That's not what the Hebrew conveys. It's just about putting on clothes, or even more neutrally, "wearing" as the Tanak has it.
"warrior's armor" is getting close to fabrication. "geber" was discussed in the previous phrase. The important word here is "śimlah" (or in the genetive construction of the Hebrew, "śimlat ʾiššâ", with the -at ending signalling an "of" relationship). It is, quite unambiguously, simply an outer garment, a cloak, and you might well sleep in it, using it as a blanket. It never has the nuance or connotation of "armour" -- this pretty much qualifies as a falsification. I can't see how it is a "mistake", when the translation is, presumably, thoughtfully and deliberately produced.
(The Greek translation, stolē, is likewise simply a "robe" - it's where we get our English word "stole" [as in "fur stole"] from.)
Given the unambiguous meaning of "śimlah", and the symmetrical construction of the prohibition, this is the clincher for why "kĕlî" does not mean "weapon" or the like in the preceding phrase.
MT: כִּי תוֹעֲבַת יְהוָה אֱלֹהֶיךָ כָּל־עֹשֵׂה אֵלֶּה
Translit.: kî tôʿăbat YHWH ʾĕlōhêkā kol-ʿōśē ʾēlleh
LXX: ὅτι βδέλυγμα κυρίῳ τῷ θεῷ σού ἐστιν πᾶς ποιῶν ταῦτα
Translit.: hoti bdelugma kuriō(i) tō(i) theō(i) sou estin pas poiōn tauta
Trans.: for every one that does these things is an abomination to the Lord thy God
GT: for to Yahweh, God of Host, disgusting is such that do so
TNK: for whoever does these things is abhorrent to the LORD your God.
Commentary: All our translations line up pretty much here, even the GT -- although it has one distortion.1 (It also is barely English, but we're not discussing the quality of the translation as 'literature', just its accuracy.)
The distortion is that the GT translation imagines some party forcing some weaker person or persons to bear arms against their will, and that this is abhorrent (it is quite right about the force of this term, tôʿăbat) to the Lord. That sense is wholly absent from the Hebrew, and from its ancient Greek translation which (translated by Jews for Jews in the pre-Christian era) had no reason to meddle in its translation of this text.
Conclusion Plainly, what is abhorrent to the Lord according to Deuteronomy 22:5 is cross-dressing. Where that leaves the relationship of church and synagogue with the fashion industry is a different question, and not one for this Q&A. The clear question posed has, I hope, a clear answer. (Actually, as I post this, it seems to have at least one other clear answer already.)
1 And one mistake: it adds "of Host", which should probably be "of Hosts", [Heb. ṣĕbāʾôt] IF it was in the Hebrew text, which it isn't.