Switzerland moved towards a self declaration system last December without basically anyone batting an eyelid (and legally recognizes non binary identities as of last month)
Broadly speaking, the trend in western continental Europe has been a rather quiet move towards better and easier recognition of trans identities, with only relatively limited pushback. In stark contrast to the USA. I mean the fact in itself that there has been barely coverage of this even within Germany and Spain is probably the best example of how much more relaxed people are about the topic in continental Europe
Or, more specifically, the equivalent emotional debate in Europe tends to centre around gendered language, which is an issue that anglophones on this here blog tend to have a hard time understanding
Tbf I think it's more the other way round, no one cares because no one talks about it and no one encounters any of that stuff in real life.
It's hard to get worked up about something if you never encounter it or even really hear about it.
I'm talking about France ofc. Maybe it's more mediatized in other European countries.
I think if culture wars are so extreme in the US, it's because each side has to make a big song and dance about all of their positions rather than try to push for their views in a more discrete manner.