That a man who thinks he's a lass is no more a woman than a LARPer who thinks he's a minotaur is actually an anthropomorphic bull is obvious.
Pointing out that the gender bender stuff is all make believe isn't the most effective way to hold the line on this latest front in the Culture War, though.
Instead, a modest suggestion for men who favor living in a society where each person feels compelled to use the restroom that corresponds to his or her biological sex: Every time you go into Target (or any other retailer who adopts a free-for-all restroom policy) and nature calls, use the women's room. No need to make a production out of it. Just take care of business and be on your way. If anyone questions you, dismissively respond with how you're trying to get in touch with your feminine side.
To take it up another level, use the women's changing rooms as well.
If enough men do this eventually critical mass will be reached and something will have to change--something radical, like maybe reverting back to the restroom policy that worked for 99.997% of the population until last week.
Parenthetically, social conservatives will lose on this issue just like they lose on every other one. Instead of a radical response like the one suggested here they'll instead try to objectively rationalize against a chorus of "why do you HATE HATE HATE trannies?!". The battle is over before it even begins.
Libertarians will lose, too, though it'll take a little longer. Tranny free-for-all restroom privileges will eventually be legislated into existence or discovered by the courts at some point in the future. Currently the issue has life because a city legislated tranny restroom protection and a state legislated conventional restroom policy in response. In the future things like this will be moot because federal protections mandating private organizations allow people to use whatever restrooms they want to use will be in existence.