Democrats want to adopt positions that they can win on.

What evidence do you have, beyond your personal biases, that, "we are going supersede the judgement of independent organizations in order to dictate policies on trans athletes to them," is a winning position?

It's better to have uniform laws since teams from different schools compete against each other.

Athletic leagues don't operate on a school-by-school basis. There are county, state, and national leagues that are already setting the rules by which schools compete. The NFHS and NCAA, for example, already made the, "uniform laws," you want. Both organizations have already been forced to change their rules on trans athletes in certain states to accommodate anti-trans legislation, and the NCAA changed their national rules to comply with a (probably unlawful) executive order.

This is what's so infuriating about your position. You act as though you're just asking for the government to make rules for everyone to follow, but you're actually asking for the government to overrule the rules you don't like.