Even if it were a public forum (which not all public events involving a government official are), I'm not sure that public forum law prohibits sex discrimination as well as viewpoint censorship. I can see an argument that it should (and that it shouldn't), but I don't recall. seeing any case law either way.
Either way, the fact that it is a private rule means it is not a public law. The government doesn't have to abide by laws you just made up for yourself on a whim. If I say "no shoes allowed on my private property" the police aren't forced to comply with that, so why would a government official at an event be required to comply with some inane sexist rule?
If you permit them to enter, and you have a no shoes rule posted, they are free to enter with shoes. Because such a sign means fuck all in the world.
http://www.legislature.mi.gov/(S(2d5ss4y1dr2wfo0uz3r0a3zk))/...
I wouldn't bet against there being some jurisdiction where it is a felony.