Football? American Football has no restrictions on gender, it’s just that no woman can compete after puberty truly sets in. What that guys says is true about physical sports. Women can’t compete and never could. I can’t think of a single sport where a woman could outcompete a man in a physical sense. Even something like gymnastics, I think men still overcome the natural female advantage that comes from being small.

Chess from what I recall created a woman’s division because of the systematic biases and pressures girls faced. However, if I’m recalling correctly, it’s not particularly weird for a woman to complete in the open division. It’s just not a welcoming place for woman, so beginners often start in the women’s division. With that in mind I don’t see why transpeople shouldn’t be allowed. They wouldn’t be welcome much either in the open division, but also I’m not sure they’d be welcome in the women’s division either, so it’s kind of a wash.