The biggest hang-up is that the impact of a trans person competing as their new gender is different depending on if the transition is guy to girl or girl to guy. Obviously, guys transitioning to girls are going to have physical advantages. Girls transitioning to guys are not, even if they've been taking testosterone and hitting the gym for years. So a blanket set of rules that allows them to compete in some capacity might unfairly impact one type of trans person more than the other.
In individual sports, I think they should be allowed to compete but their postseason results (or however each sport does it) just aren't officially recorded. They can't compete in tournaments, they can't hold records, but they can earn W's and L's in the regular season. This obviously sucks for girls transitioning to guys because any ability to qualify for tournaments or postseason championships would be a pretty impressive accomplishment. But, on that same token, they would likely be taking a supplement that is technically a performance enhancer, even though testosterone supplementation would really just be catching them up rather than vaulting them ahead. Still, maybe the blanket rule in this case isn't as unfair as I originally thought.
Team sports are a little trickier. Where it's not a problem to have guy-to-girl athletes piling up regular season wins in individual sports, because they wouldn't be eligible for postseason and wouldn't be taking a spot away from anybody, it would be a problem in team sports. It's not fair to not let trans people compete and it's arguably cruel to force them to compete as their old gender, but it's also unfair to allow a team to potentially earn a postseason spot over another team because they had a trans person helping them (sticking with the guy-to-girl example). The team might get bounced early in the postseason once the trans person is disqualified from competing but that doesn't help the team they replaced, that was one spot removed from postseason eligibility. Removal of a girl-to-guy athlete for postseason play would probably be a non-issue from a competitive standpoint.
An interesting caveat to this comes into play with sports that aren't available to both sexes. In these cases, the rules governing transitioning/transitioned athletes should remain the same as the rules governing non-trans athletes who are simply the opposite sex of those competing in their sport. Field hockey is a good example. In the US, field hockey is almost universally a female sport; boys teams are rare, if they exist at all. When I was in HS, our field hockey team actually played against a team with a boy on it. He was an exchange student from a country where male field hockey was common and I think Title IX (something like that) required that he be allowed to play because the sport wasn't offered for his gender. In scenarios like this, I think it's obvious that trans people should be allowed to compete without restriction.
Physical tests to see if M2F athletes aren't too strong/fast and if F2M ahtletes are strong/fast enough have been proposed or are in some form of existence, but these create more problems than they solve, imo. Also, if anybody is worried that males would take advantage of gender transition simply to earn trophies and records competing as a girl, I don't think that's a legitimate fear. If you're not actually transsexual, you're not going to say you are just so you can win stuff as a lady.
In individual sports, I think they should be allowed to compete but their postseason results (or however each sport does it) just aren't officially recorded. They can't compete in tournaments, they can't hold records, but they can earn W's and L's in the regular season. This obviously sucks for girls transitioning to guys because any ability to qualify for tournaments or postseason championships would be a pretty impressive accomplishment. But, on that same token, they would likely be taking a supplement that is technically a performance enhancer, even though testosterone supplementation would really just be catching them up rather than vaulting them ahead. Still, maybe the blanket rule in this case isn't as unfair as I originally thought.
Team sports are a little trickier. Where it's not a problem to have guy-to-girl athletes piling up regular season wins in individual sports, because they wouldn't be eligible for postseason and wouldn't be taking a spot away from anybody, it would be a problem in team sports. It's not fair to not let trans people compete and it's arguably cruel to force them to compete as their old gender, but it's also unfair to allow a team to potentially earn a postseason spot over another team because they had a trans person helping them (sticking with the guy-to-girl example). The team might get bounced early in the postseason once the trans person is disqualified from competing but that doesn't help the team they replaced, that was one spot removed from postseason eligibility. Removal of a girl-to-guy athlete for postseason play would probably be a non-issue from a competitive standpoint.
An interesting caveat to this comes into play with sports that aren't available to both sexes. In these cases, the rules governing transitioning/transitioned athletes should remain the same as the rules governing non-trans athletes who are simply the opposite sex of those competing in their sport. Field hockey is a good example. In the US, field hockey is almost universally a female sport; boys teams are rare, if they exist at all. When I was in HS, our field hockey team actually played against a team with a boy on it. He was an exchange student from a country where male field hockey was common and I think Title IX (something like that) required that he be allowed to play because the sport wasn't offered for his gender. In scenarios like this, I think it's obvious that trans people should be allowed to compete without restriction.
Physical tests to see if M2F athletes aren't too strong/fast and if F2M ahtletes are strong/fast enough have been proposed or are in some form of existence, but these create more problems than they solve, imo. Also, if anybody is worried that males would take advantage of gender transition simply to earn trophies and records competing as a girl, I don't think that's a legitimate fear. If you're not actually transsexual, you're not going to say you are just so you can win stuff as a lady.