I'm in Greece so I can comment on the situation here (and with the language).
There is still a preference for the use of the word "transsexual" here to refer to anyone MTF but a lack of understanding that FTM can also happen. Most people believe that anyone who falls into this category has had complete genital surgery and hormones and is likely gay (with respect to their birth sex, that is; meaning, a biological male who is attracted to other biological males). Many people use the word for 'transvestite' completely interchangeably with transsexual, including newspapers. There is very little understanding of what trans means in 2018, here, which is probably how we ended up with self-ID for anyone 15 and up, enshrined in law, with pretty much only the Church and the communists objecting.
In the language there are two words that are used within the LGBT community, one meaning transsexual and the other transgender, referring only to roles and stereotypes. Most people don't know these words or use them.
As for the word "woman", it only means woman here; and "man" only means man. I have yet to see anyone try to claim that the word 'woman' in Greek actually includes transsexuals or transgendered people identifying as women against their sex. But it almost certainly does happen within the LGBT community (which I'm not in). We hear a lot about oppression of trans people despite them actually having additional rights in law that literally no one else has, but I haven't actually heard complaining about 'language exclusivity' so far.
It's a language where almost every word in the sentence reflects grammatical gender so if someone is making you use pronouns against your linguistic instinct, it becomes almost impossible to speak. I've yet to come across this in real life here, because sanity continues to prevail in the smallish town where I live.