Maybe I'm missing something, but isn't sex is based on chromosomes at the point of conception, it is not something which is "assigned at birth"? Obviously there is the rare people with DSD but I see this as a totally separate issue to the trans debate (although there may be some crossovers in that some DSD people may be trans).
I personally think that gender is fluid and people can change their gender, but that sex is a biological thing which cannot be changed.
Trans people should have exactly the same rights as everyone else, no question about that. There is a dichotomy here though where it is perceived that by granting rights (in this case the battle ground seems to be over sport and changing facilities) to one group you remove rights from another group. This also cannot be right.
As a male person I don't feel that I should be saying to a female that the changing rooms thing isn't an issue, it's not my place. But that is clearly difficult for trans people who have to either use the male changing rooms (which isn't acceptable imho) or disabled changing rooms, which probably makes them feel isolated where we should be trying to be inclusive and welcoming to people who have probably gone through significant mental trauma to get to the point they are at. I genuinely don't know what the solution to that is. Individual cubicles for all in a unisex changing space? Swimming pools certainly seem to be going down this route and it works quite well.
The sport issue is a bit more clear cut in my opinion, clearly someone who has gone through male puberty and years of male physical development cannot just reverse the effects of that on their body. There is a reason why most sports are divided into male and female sports, because male development leads to physical differences which in general would give males the advantage over females. I think that it is clear that this advantage is retained to some extent despite reductions in testosterone levels. You can see from the results that Laurel Hubbard is getting in weightlifting that she has a significant advantage over women who are biologically female.
https://twitter.com/Scienceofsport/status/1399449040660615171?s=19
I have to read up more on this as there must be more to it that "just" changing rooms and sports, people can't be getting so worked up about it over just that surely.