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
I will note that the debate in Spain debates on trans people haven't exactly flown under the radar either. In fact, it is one of the biggest differences between UP and PSOE, with UP being in favour of the new Trans Act and PSOE taking the usual TERF arguments (obviously the conservatives all oppose it for the reasons you may expect). Only rent control has as big of a divide between the 2 coalition parties.
However, the fact that while it is a huge debate, it is an internal debate within the government as opposed to a debate between the government and the opposition means that it is slightly less divisive and not as prominent compared to debates on say, taxes or "Spanish Unity/Catalonia" which are a much bigger part of discourse in Spain.
For what is worth, I tend to find the divide between pro-trans activists and anti-trans feminists to be one mostly based on age; with older feminists being against trans recognition and younger feminists being in favour. Of course the old vs young divide matches almost perfectly to PSOE vs UP here within the left.
I do agree with you that the issue is much less prominent in continental Europe (including Spain) than it seems to be in the USA or the UK; but at least here it isn't exactly 100% quiet either.
