Maybe, for "rec league" or whatever, but school teams are usually meant to be competitive, and non-gendered sports would mean girls wouldn't have equitable access to athletics.
But even for non-competitive teams, girls are unlikely to be able to access shared sports to the same level as boys. At a ~~party~~ high school I worked at, there was a major challenge with girls being willing to access open gym time, feeling uncomfortable advocating for access to basketball nets for practice—even girls who were on the competitive team felt they couldn't use open gym time.
TL;DR: Sexism runs deep. We need policies that recognize that and build equity, not just offer "equality" that perpetuates, or even magnifies, the problem.
I sure as hell didn't know what it was when I was 20. I think I only learned about all this shit when I was teaching a student who had a confederate flag phone wallpaper (not in the US, btw), and I did a "crash course" in other to look for that are subtle symbols, like 1488 and lesser-known Nazi/white supremacy logos.
Some of them are super generic, too, like the one that looks like two parallel square-ish lighting bolts, or the square-looking ankh thing. (Someone linked a list above, of symbols banned in Germany).
Seems more likely that the establishment is trying to smear a progressive candidate than that a progressive candidate is secretly a neo Nazi.