"In a letter filled with rabbinic sources, Selden provides a loophole based on Maimonides, with a foundation in the original Hebrew biblical text: the prohibition does not apply to cross-dressing per se, but rather to ancient idolatrous rites whereby male priest worshiped Venus in women’s clothing and women worshiped Mars in armor."

Harold Torger Vedeler's "Reconstructing Meaning in Deuteronomy 22:5: Gender, Society, and Transvestitism in Israel and the Ancient Near East" (Journal of Biblical Literature, 2008) makes a similar argument, identifying it as a prohibition against cultic behavior (worship of Ištar rather than the God of Israel) reinforcing ancient Israelite categories of masculinity. What Vedeler describes in terms of Mesopotamian cult practice is not identical to what Selden reports, of course, so now I want to read Maimonides for myself.