These kinds of bills should be non-controversial when you remove the element of partisanship and everyone's desire to "smite one's political enemies"
In terms of raw opinion polling, on paper, this one should be a no brainer.
A person has to be really dug in on a political agenda to look at some of the situations we've seen and conclude "it's completely fair for a person who was born male to complete against someone who was born female"
There are certain sports where it doesn't matter. (I don't think anyone cares if a transwoman is playing billiards against biological females) But I think there are more sports where it does matter, and people tend to deflect from what we know about biology, and opt to push for things in the name of inclusion that go against common sense.
Bathrooms and pronouns are a different conversation, and all of the various facets of this conversation shouldn't be bundled together as a "package deal". I'll call someone "she" if they identify as a woman, I don't care what bathrooms people use. The changing room situation gets messy (for both sides of the argument), but the [physically demanding] sports thing is a no brainer as I see it.
We know (via science) that hormonal interventions (while successful in changing future development and visual features) does very little to diminish the physical advantages that biological males enjoy.
A years worth of suppressing male hormones only decreases the male strength advantage by 10%, and two years worth of suppressing only decreases the male speed advantage by around 5%.
For trans men, the story is a little different. After 2 years of gender affirming male hormones, they can close the gap a lot more (despite still being at a disadvantage in terms of other factors) compared to their biological male counterparts. But when having the trans sports debate, nobody's really concerned about the trans men competing against biological men. It's the other scenario that rightfully gets all of the attention.