Contrary to what Pro-Lifers will tell you, the majority of the Americans of all races supports legal abortion, except White Evangelicals (yes, even Catholics who like to present themselves as sooo traditional and so much better than the Protestants). Also, the Boomers who everybody loves to hate nowadays, are much more conservative in their views on the issue:
That includes 60% of the moderate Republicans, 72% of "conservative" Democrats and nearly 60% of the men. These views have hardly changed in 30 years:
In other words, liberalism still enjoys a broad support in the USA, and I presume in other Western countries, too. You can blame the elites, the bankers, immigration, "special people", the mass media and whatever you wish. I blame the lack of faith:
As you can see, 97% of atheists support it...
All graphs taken from here.