I think this is a social issue that will take quite a long time to figure out, especially since - unlike certain things like ancestry - there really isn't any way to validate somebody's "gender identity", and such may be very different from one's "physical development" especially depending on what steps one might to do to transition, and when.
Some things are simple. Don't harass or attack people based on their gender identity should really just be a subset of "don't be an asshole", but there are plenty of people who already have problems with that in general.
Stuff like gender-based sports where physiological differences in body development are a big part of WHY those sports are segregated by gender ... that's less easy.
For example, the cases of Anne Andres in power-lifting or Lia Thomas in swimming. Cycling worldwide only allows transgender athletes if they transitioned before puberty. I'd expect that many other sorts will decide to delineate between gender-identity and biological gender with a time-bias such as in the latter case. Semenya was temporarily prevented from running competitively due to supposed "high testosterone levels", with lots of speculation - often cruel - about her gender. Meanwhile, the IAAF put in policies to use testosterone as a deciding factor.
This is even more complicated though, as it's also at many levels an issue of self identity, and we've already had plenty of scandals regarding people who falsely claimed cultural identities etc for their own benefit. There's no way to claim a gender by ancestry and issues such as testosterone may be quite inexact (not to mention invasive) to make life-affecting decisions.
All of these are edge cases that some use to stoke the fire, to the point where battle lines are drawn overall over what defines a man or make versus a woman or female, and politicians are some of the worst of them all for making it an issue of blame and political currency with their base. While there are some who may honestly want more science for selection in i.e. sports, there are plenty who have simply extended it with their existing bias against something as simple as "boys in dresses" or "girls in trades".
With shouting and accusations on both sides, it's hard to hear any reasonable argument over the noise and accusations. Small wonder maybe since we're only a few generations since people of all races were allowed to vote in certain democracies, and there are even less since women could, but some of the shouts, prejudices and battle cries are likely much the same.
I honestly don't expect my parents to get it at all, though I'm hoping they've enough sense to just stay out of it rather than attending any rallies etc.