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I imagine the male and female character models are shaped differently and have different animations, so it would be more work to make the clothes cross-compatible, while 90% of players won't want to. By comparison Animal Crossing, which allows cross-dressing, has much simpler character models and the animations are identical.
Although there are rumours the Japanese version allows crossdressing, I haven't seen a source or screenshots so I doubt it.
Also prepare for shitstorm. Most of 4chan hates us traps.
