It doesn't say not to look like the opposite sex, but not to wear clothing that is for the opposite sex - such as men wearing skirts and dresses, and women wearing... pants...

Before anyone says that was OT and no longer applies, do a trace of the word "abomination" (in the context of what is an abomination to God Himself), and show where any of those abominable things/sins are done away with. If they are not, neither is this commandment.