Does Deuteronomy 22 forbid crossdressing or being transgender?

Surprisingly little has been written on this so far. The modern concept of gender identity is still very new, and there’s been very little discussion of it in Christian spaces before the last few years. As transgender issues have recently become more controversial, some Christians have pointed to a single verse in Deuteronomy to condemn transgender people. However:
a) Christians do not generally consider Old Testament law to be binding on us today.
b) The passage is about crossdressing, not being transgender.
c) Scholars have argued it’s not even about crossdressing in the modern sense.

For example:

• Harold Torger Vedeler at Yale University says no. He wrote for the Journal of Biblical Literature in 2008 that the Hebrew words in Deut. 22:5 addressed not crossdressing in general, but specific situations in Israel at the time: “The Israelite conception of transvestitism was not the same as transvestitism in modern Western culture; it was based on a cultic tradition absent today….” See his full article here.
• Christian researcher Kathy Baldock agrees that the passage isn’t about crossdressing or transgender people. Citing Jewish rabbis, she writes that the passage is about “wearing the clothing of the other sex with the intention to deceive.” In this Canyonwalker Connections article, she points to three possible interpretations of the passage, none of which are about being transgender.

This shouldn’t be a surprise. Prior to modern debates about transgender people, Christians have generally not had a problem with people dressing as the other sex (e.g. in plays, for comedy, at Halloween, etc.). In fact, popular films like Some Like It Hot, Yentl, and Mulan all depict people disguising themselves as the other sex, but they weren’t widely condemned by Christians at the time.