Not only abortion, some EU countries still have laws to discriminate people based on their sexuality. One recent example is that one of the prominent openly gay German politician (Jens Spahn) had to give up his position (although he had it coming because his other political scandals) because he used a surrogate mother in US to have a kid with his husband. I didn't know till then, but apparently surrogacy is still illegal in Germany and nobody was talking about making it legal and let women decide what they want to do with their bodies.
All those democrats and celebrities in US wants to move to European countries and I would love to see their faces when they realize that old world is still archaic in so many aspects.