I think this is one of the few times where it may be a bit of a valid double-standard, tbh. I mean, with typical men's clothes being more casual and acceptable for both genders to wear (shorts, shirts, loose pants/trousers, trainers etc... even smarter like suits) no one really gives a **** or looks twice if a woman wears these things. But put a dude in a skirt or heels or a blouse or whatever and it'll cause a lot more negative thoughts.
Personally I like a girl that doesn't fit the typical girly-girl bill and will wear whatever she wants, especially if it's for practical reasons - shows an understanding of logic ("I don't care - they're comfy!") and a somewhat unwashed brain (does that make sense? Not brainwashed). I think yeah if we're going out for a meal somewhere nice then let's both dress up and look sharp but if we're bumming around the house or walking in the hills then wear whatever you want, just don't be a noob and wear idiot shoes if we're doing the latter
In response to the OP, I think it depends whether he wanted to do this in public or if it was an in-the-bedroom thing. I wouldn't care if my girlfriend always dressed like a guy but I probably would have a difficult time with it if I were female and my boyfriend did it. As much as I'm all for equality, that's just how I feel about it, that it would be harder to accept.