OP, unfortunately your more nuanced take (which I share) is largely lost in the conversation. The loudest voices on each "side" of this issue tend not to be reasonable (understanding of physiology) or respectful (understanding of sociology/human rights). This is unfortunate because it means that those who feel that sports classifications should be based on sex (not gender) are vilified or dismissed as bigots/TERFs, even if they are supportive of trans rights more broadly.
In almost all situations in society, classifying according to gender (or having no classification) is the most sensible option as most classification exists for reasons relating to social/cultural norms, ie. somewhat arbitrary/about presentation. There are a small number of situations where physiology is the primary reason for separation, and in these situations it can be justifiable to separate based on sex. I'd even argue that in sports this only really applies to higher level adult sports. If I showed up to a women's beer league community soccer league, I wouldn't care if some of my fellow participants were trans. The purpose of the women's classification there is to encourage women's participation since some women feel uncomfortable socially in mixed leagues. This includes transwomen, so their participation in the community/rec women's league makes sense.
But, if one paints the picture that all those who oppose sex-based classification in competitive sport are inherently bigots (and amplify/strawman the actual bigots who share this viewpoint but for the wrong reasons), it is easier to dismiss this view without discussing the valid points about the permanent physiological advantage given by male puberty, and the importance of maintaining meaningful competition categories. People who are spewing hateful or derogatory stuff (misgendering, deadnaming, classifying being trans as a mental illness etc.) must be disavowed.
Unfortunately this doesn't seem to always happen, or the bigots champion someone who is presenting purely scientific arguments, which along with the vilification, tends to result in more reasonable and respectful voices being drowned out. Plus, since the forums are anonymous people feel they can get away with things that they'd never say irl or in an identifiable context.
Irl, most of the people I talk to quietly have a position similar to mine, or feel that although there may be an advantage that inclusion (gender classification) is more important. Though I may not agree with the latter entirely (agree inclusion is important, disagree with solution), this is at least a reasonable and respectful point of view with which one can debate. Online is a dumpster fire.