Ireland quietly passed the GRA with no public consultation that I can find, and in the wake of the euphoria following the success of the Gay Marriage Referendum.
It seems that here transgender means the old-fashioned desperate transexual - the person who will go to any lengths to "pass", not the in-your-face transactivists that seem to be rearing their heads in the UK.
Having said that, transgender is creeping into universities and other organisations. At the moment the idea of a "third space" seems to be acceptable all round. If that changes and transgender people become more aggressive about women's spaces, public attitude might change (or at least people might notice).
I think it's sport that'll focus people's attitudes here. There is a big push to get youngsters into sport and special consideration for women. If transwomen appear in women's sport people will notice.
Abortion is a whole other story [sigh] Don't get me started on that one.