It seems too many people, on all sides of the issue, fail to address that this is really two separate issues we're talking about and your stance on one doesn't necessarily predict your stance on the other.
Are trans identities valid, and should we address people by their preferred name and gendered pronouns - this is one question, and I've made clear here my stance (yes, we know that nature isn't as rigid as the framework we use to understand it, we should be open to things not fitting into a rigid framework, we know that cultures across time and geographical space have had concepts like transgender/nonbinary indicating it's a natural phenomenon. If my friend used to go by Bill and asks to now go by Barbara, it harms me none to respect this.)
Should trans women compete against cis women in sports - this is a separate question. I lean toward no. I think sports are (or should be) separated on the basis of biological sex, not on the basis of gender/gender identity. I see no reason why competitions should be segregated by gender/gender identity - it makes little sense to do so. It DOES make sense to segregate them on biological sex - we have women's tennis, women's basketball, women's soccer, etc. because men are generally bigger, stronger, and faster and especially at high levels like professional and scholarship college competition, you'd have few to zero women able to compete against men. I acknowledge the complications here that arise from the small fraction of people who are biologically intersex, and don't have an easy answer to all that arises from this.
There are further questions that arise beyond those two, and the entire issue is far more complex than, again, can be reduced to an easy-to-digest binary where you either treat trans women identically to cis women in all respects, or you reject trans identity altogether and treat people as the gender they're assigned at birth in all respects. I'm generally respectful of trans identities, and have been called a woke leftist idiot over it. I also would have no interest in dating or having an intimate relationship with a trans woman, and have been called a transphobe over it. Things aren't ever actually as simple as the mental frameworks we use to simplify a complicated reality.