Are you not allowed to support certain policies of one party and certain policies of another party? Especially if you live in a different country, so you’re not voting for either of them anyway?

I never even implied that. You came to a meme about American politics and asked how the two topics were related. Sorry not every meme is custom-made for you.

In most sports, there is no such thing as “men’s” sports.

… are you serious? All the most popular sports, running, swimming, weightlifting, football (American and the rest of the world), basketball, hockey, cycling… I decided to check out the Olympic’s website for some other examples and almost all of them have hard gender divisions. A few don’t but the vast majority are divided. Chess has an “open” and a “women’s” division as you describe, but again, it’s because the gap exists thanks only to a dearth of women playing the game in the first place. This is not the case in most sports. Trans women who have undergone sufficient hormone therapy do not have an advantage, and should be allowed to participate.

why not just go there and leave women’s sports, which are explicitly created to make it possible to compete well without having been born with a male body, alone?

People rarely just choose what they’re passionate about like that. This is an incredibly flimsy excuse to exclude people from competing in what they actually enjoy doing.