I suppose it takes as many to tango as to polarize, so I couldn't say which one I find more dangerous. But it's clear that--as usual--people are having difficulty listening to each other while shouting. And I'd say that benefits those who wish to keep things under their control.
This is at least three questions wrapped in the guise of one.
1. I think polarisation has the potential to become dangerous but has not yet reached that point. I would regard the highest danger as the point when polarisation is so great that it triggers civil war and bloodshed. But it has reached a point where it is making democracy less functional, less effective as a form of government.
2. The extreme poles of left and right have not shifted position. The extreme right still has the same goals and has merely become more sophisticated and complex in its methods. The extreme left has fissioned into multiple forms of leftism, from traditional Marxism to variations on anarchy.
3. The majority of democratic countries have slid right over the last 40 years, the left by about 5º and the right by about 15º.
One could argue that part of the problem is that the division between left and right is too equal, too close in numbers, leading to hung parliaments. If the government's majority is low, it makes it harder to pass legislation. Post-war Germany has had hung parliaments for so long that they have learned to negotiate amendments and compromises. In a way, this could be said to better represent the majority preferences of its people.
I don't think it matters which side you choose if you aren't willing to meet somewhere in the middle. It's the polarization that is dangerous, not the side.