Broadly speaking, you probably agree with the large majority of the views commonly attributed to whichever group you identify with - what are the exceptions? Something that if you mention without a caveat immediately makes people jump to conclusions or even attack you?
I think, and this may be a wild concept that bothers both sides of the discussion, that individual sports governing bodies (specific leagues, NCAA, etc) should be making the decisions and absolutely nobody in government should be involved.
People should be allowed to compete in sports, but it should be up to the individual sports governing body to decide how they slot people. And if there is an absolute ban in the league against use of hormones (aimed at preventing performance enhancing effects), then so be it. Those bans were in place prior to the trans people in sports discussion, I wouldn’t say they are inherently biased. Take up the language of the rule with your local league to allow for medically necessary hormones for specific issues (including gender dysmorphia), but it is ultimately their prerogative on rules for their league. A senator doesn’t need to weigh in.
But any poltician who so much as brings up trans people in sports should be immediately told to stay in their fucking lane.