Actually American views on homosexuality weren't much better than European views back in Turing's time. If Turing was American back then, I doubt he would have faired much better.

Anyway, comparing modern European views on homosexuality to modern American views, well, yes, European views are much less "prudish", though of course this varies from country to country. After all only in Europe do you get openly gay extreme right wing politicians who say things like "to us homosexual relationships are the same as heterosexual relationships" as an excuse for keeping Muslims out of the country...