NAH as described. That said, I think you should reassess your own thought process.

Did you suggest that a female should be included because you think it will add genuine value to the show, or is it just a question of gender inclusion? Comedy is subjective, but if the roster is limited and the males that have been selected tend to get more laughs than the females, then is there a reason to add one of the female comics?

You mention you'd be thrilled to call them a female for an all-female show, but

to call them the only woman on the show when they don't even bill themselves as a woman just didn't make sense to me.

Is anyone calling Sid that besides you? Would Sid be advertised as such (only woman) on the promotions, or would it just be "Comedy Show featuring x, y, Sid, and z?

It just feels a bit like you may have arbitrarily decided that the show needs a female comic in place of (or in addition to) the males. "Gender identity" and non-binary identities are a concept that everyone is still getting used to, and I don't think you're wrong for having the reaction that you did.

Stand-up is tough, and men and women often have starkly different material, but funny is funny. Your friend should pick the funniest available comics to go on the tour (based on audience opinion, not yours/his) and if one or more of them happen to be female, then that's great. If Sid is one of those females, awesome. But if there are funnier male comics to be booked, then maybe the show shouldn't look to add a female into the mix for no reason other than claiming to have included a female.