Those who go against the norms of their culture in general can face similar problems, regardless of whether those norms are conservative, liberal, or something else.
Join a progressive, tree-hugging, vegan commune and then a few months later post a series of selfies to Facebook of you driving a Hummer through the McDonalds drive-thru and then eating several Big Macs, and you'll be in for some world-class shaming and shunning. :-)
The greatest time for the middle class in the United States, for example, was in the 50s, when society was much more conservative than it is now. (That's what the "Make America Great Again" is all about.) The 50s are the last decade that the conservative WASP aristocracy was in power. Every election since, groups like African Americans, women, and Jews have increased their power and brought about with them big government. How is that an improvement? Surely, you agree that big government is disastrous for the country?
There's a book "Sex and Culture" by J.D. Unwin that actually argues (convincingly in my opinion) that a suppression of sexual energies (i.e. control of women) is a necessary (not sufficient) condition for a civilization to succeed. Check it out.
Wait, what were we talking about?
Even if I take your point that big government can be good, one has to concede that it succeeded with social conservatism. Ever since social liberalism took hold, things have gone steadily downhill.
If they don't suffer from such unpopularity somewhere, then they seem to have all the cards in their hands.