sports are some sacred thing whose purity must be protected

With that framing, I agree. But that's a strawman. Most people don't care for the romantic vision of a "pure" sport but rather, the general idea of keeping sports fair for kids. 1/2 the rules in all sports are about keeping things fair. Age buckets, weight ranges, gender, a system of leagues (ex varisty vs JV) to sort players on skill level, and so on.

So if you assume that there are biological differences between men and women that affect fairness within a competitive sport and if you feel those differences largely do not go away until after some form of medical transition and if you think sports are important in kids lives & keeping them fair is important - then you vote the way blue WA did.