The general public are unlikely to take this seriously. Who is going to compete in this third category? Women are unlikely to compete in it because they stand to be outclassed by any men entering the category. Men will be similarly unlikely to compete because there is likely to be higher prestige in men-only competitions.
The whole thing will revolve around game theory, where every potential participant will weigh up the likelihood of winning, personal pride, and monetary or publicity rewards.
What you'll end up with is a bunch of transgenders participating with a minute niche following. Then they'll start complaining about "cis privilege", or whatever, because nobody (and hence lucrative sponsorship deals) will take them seriously.
Similarly, people converting have their own sporting characteristics, and we should work to find ways to include them as well.
As such, we need classes that distinguish between different levels of de facto biological advantage: a completely open category would still be dominated by males.
I don't understand why would people find different martial arts weight classes normal, and not even entertain the thought that this might apply to other sports as it pertains to other genetic and acquired traits.
The fact that those are orthogonal today matters exactly how (when talking about introducing more granularity at the first, gender level)?
So I would guess that having two categories, "open" and "bona fide female", would make more sense.
Also, in tennis, do you call the "open" category "open" or is that too confusing as the word "open" is already used in a different sense?