Free speech, and not forcing people to lie is definitely good.
But... the general EA principle is sound: avoiding discrimination unless it is justified to prevent greater injustice, greater harm.
We want to protect women's single sex spaces - where they are needed. But I'm all for challenging remaining unjustified barriers.
Beauty pageants are weird. They judge people on how closely they conform to a very specific, regressive-gender-stereotype ideal.
Is that a reasonable thing to do? Certainly not in wider society /for anything that matters. Should it be allowed as an entertainment event? Probably. There's some social harm, but probably not more than MMA say.
So, should transwomen be excluded from that beauty pageant?
Well, the entrance criteria include some pretty strong 'plausible virginity' criteria. If you allow that kind of reproductive control in the criteria. it's not really a stretch to exclude males.
Personally, I find that that control distasteful, and think that both transwomen and mothers should be allowed to enter. No one is harmed if they do (so long as no one has to pretend that the transwomen are actually women). The 'winner' characteristics can certainly apply to both.
The regressive gender stereotyping which being Trans is based on is actually a pretty good fit with beauty pageants!
Of course the changing facilities should be kept single sex!