I have mixed feelings on this. I think transgendered women deserve respect and understanding and to be treated as women.
But for a competition like this, it's a fact that their bodies are not the same, exactly, as women from birth.
There's nothing wrong with it but I can understand a group, women, being concerned about someone not exactly in their group competing.
Now, for a beauty contest, it's hard to see the TW having any unfair advantage - I'd expect it to go the other direction, and why not wish them well in winning?
Of course one element of a beauty pageant is attractiveness to straight men and lesbian women, and many of them - however beautiful a TW is - won't be 'attracted'.
And that's a sort of business issues about the purpose of the pageant. Then again, if a lot of the audience doesn't like, say, black women in, I don't like that - so...
I'd let them in, I think.
On the other hand, more athletic competitions seem to raise more issues, if they have an advantage as a TW. That's come up in a sport such as golf. Hard call.
Fighting discrimination good; encouraging discrimination if it's undair causing resentment bad. There aren't enough to form a 'transgeder tournament' really, are there.
I think I'd leave that one up to the science - if unfair, no, if fair, yes.