I read some research a while back about the physical differences between trans women vs. "natural" women. The study used running as the testing metric.
Basically, if hormone therapy starts early enough, there is no real physical difference between males and females. The study did however show, that men who have already been through male puberty, then transitioned to female retained some physical advantage. The advantage also depended on how long the transitioning female had been on hormone therapy.
I don't think this is really a big enough problem to worry about over all, maybe put an * by the record, or start a special record keeping category for trans athletes.
As far as the MMA thing goes, all it takes is for natural born women to refuse to fight and the trans fighters career would be over.