As zoo noted, the problem with your statement is that “the left” hasn’t ever advocated for all non-transitioned individuals to compete in women’s sports.
The right has sufficiently distorted the narrative such that allowing ANY trans person—including those who’ve transitioned—to compete is seen as allowing hulking aliens to win competitions by smashing the poor dainty little ladies.
The left, meanwhile, has steadily said that (a) this is a non-issue on the state and national level, given the tiny, tiny, tiny percentage of trans athletes; and (b) as such, this is an issue better left to individual governing bodies of sports, who can determine rules at a community, regional, state, national, or international level.
I don’t think lefties on the whole are against regulating competition based on testosterone levels or other measures—but it makes a much better emotional argument to pretend (as the right does) that there are black-and-white lines that should never be crossed under any circumstance, and that trans people are disgusting and shouldn’t be allowed to use the bathroom or participate in sports.
This works to the right’s advantage, because most “swing voters” really don’t know what transgenderism is, and are scared by it. So they’re comforted by the right’s black-and-white approach, instead of the gray areas proposed by the left.