The battle lines have shifted. It's now nationalism vs. globalism, not conservative vs. liberal. It turns out that the elite, while split between conservatism and liberalism, is firmly in the globalist camp. The people tend to go the other way, especially once the hollow veneer of political correctness is shattered (terrorist attacks, migrant crises, and economic downturns can do that).
You're seeing it in Britain, where Brexit crossed party lines. The people were told they couldn't have a say on immigration or many other aspects of their lives. Britain's cultural identity, their nationhood, would just have to give way over time to a pan-European globalized society. They were told that high-minded technocrats in Brussels, not the British nation, should run their country. It turns out that the common people don't like that deal.
You're seeing it in America. Trump is not running on a policy platform. He's signed up to enough conservative pieties to get the Republican Party behind him, but his whole campaign is really premised on kicking out the ruling elite and restoring government for the interests of the American people, not the establishment and their globalist agenda. Regardless of whether you agree that his policies will accomplish that, there's no denying that that's the core sentiment that he's tapping into. This is the quote that seems to be extremely popular among his supporters: "We will no longer surrender this country or its people to the false song of globalism. The nation-state remains the true foundation for happiness and harmony. I am skeptical of international unions that tie us up and bring America down."
You're seeing it in continental Europe, with nationalist parties pulling supporters from both the establishment conservative and left-wing parties. Marine Le Pen's National Front has a very good chance of winning the election in France next year. Her platform isn't right-wing or left-wing, it's nationalist and seeks to preserve the culture of the French nation, including their social and economic model.
Alternative for Germany (AfD) is gaining rapidly in reaction to the disastrous decision to allow migrants to flood into Germany. They have benefit in the polls at the expense of both the main left and right parties.
The supporters of these movements are unified in one thing: a love for and desire to preserve their nation's culture and values, which they perceive to be under siege from uncontrolled immigration and globalization.