When it comes to sports, I think there are grades of concerns that are then confounded by transphobia. Figuring out someone's concern is part of unmasking the transphobia (and its intensity). And balancing against transphobia will be a sense of 'fairness' to people anyone disadvantaged by changes as well as a latent concern about people who will abuse changes.
Sports are weird. We all acknowledge that there's 'natural' advantage (hence weight classes in wrestling). But we also want heart and dedication to be key factors in success. We're rooting for the people who started when they were five years old and gave up alcohol and relationships in favour of daily practice. (And yet, lol, we want people to have healthy personal lives and yet will support the above). The above is then balanced against the evidence of what biological factors are actually at play (and honestly, we're in the "four minute miles are impossible!" stages of this discussion).
1) people claiming TG status to compete at an advantage, and gatekeepers being unable to keep them out. The most shameless sociopath wins.
2) people claiming TG status but delaying transition in order to compete at an advantage.
3) biological heritage creating an advantage despite transition efforts that cannot be 'outcompeted' by dedication and effort.
Now, with '3', it's all just variants on a theme. As a 'naturally' stocky person, I have no chance at professional swimming. Even if I was the 'heart and dedication' guy, I'd never be anywhere near competitive. I'm just not built that way. '3' is just that story again, just (maybe) more obviously. As pointed out previously, the same people trying to keep control over women's sports are the same people who'd not let someone transition early enough to make a difference. They're aggravating their own dilemma.
'2' is interesting, and my suspicion is that it's where the majority of the actual battle will be fought as the years of discussion turn into decades of discussion. Sadly, there are gatekeepers needed in any sporting event, which means that a 'minimum level' of transition effort would be necessary if there was too much of a latent advantage created by not doing so. In real life, subtracting a negative isn't the same thing as adding a positive (even if it's mathematically similar). But, if some hormone creates advantage, then we have a weird situation where we tolerate it if it's 'natural' but won't if it's "artificial". Sporting success is dominated by genetics, and we're just figuring that out.
'1' is troublesome because the number of people with sociopathic tendencies will be a significant percentage of the total number of people who will try to test any new rules creates. It's just simply a numbers game, but it's a real one.
*There's a weird set of intuitions here, and every individual will struggle with their own heuristics. There's a weird thing where you can 'count victims' and then assigning a relative suffering to each victim of a policy change. People who're concerned about my 3 points creating advantage will count victims. On the one hand, you have a person who'll never be able to compete successfully if the rules aren't changed (so .... "the same status as me" if you're callous or trying to be neutral) and if the rules are changed, then you have three victims (gold becomes silver, silver becomes bronze, and bronze becomes a participation trophy). And then when we do privilege-stacking (whose math is inscrutible), scenario 3 means that someone who's life is rough has advantage over people who're probably lucky people. And in scenario 2 and 1, we have someone behaving in anti-social ways in order to dominate over people who've put their heart into the thing.
- The '3 victim' scenario require an 'unfair advantage' that somehow resonates in someone's head when they're thinking about it. We're gonna be yelling about that factor for awhile, I think.
Nothing but net. The fundamental fights don't change 
