Also, I believe that we're constantly hearing so many voices trying to convince us one way or another, that our own discussions on those topics end up being attempts to convince others. That would explain "safe spaces" to some degree -- people don't want the pressure of having someone else try to convince them of something they don't agree with.
Some of it just the two-party system. The points don't matter, just which side of the line each person is on. I wonder if more parties would help depolarize the situation. I'm really not sure.
In my experience, it's more that people don't try to convince. Hell, the people who need safe-spaces, and the people they're trying to be "safe" from, don't even share the underlying epistemic assumptions that would allow them to "convince" each-other of anything less clearly observable than the sky being blue. The latter group, the people who other people need to be "safe" from, usually just scream, berate, harass, and often resort to violence.
(Note that I've avoided identifying "which side" is which. The answer is: it depends which side is dominant in your particular area. Boston and San Francisco and Brooklyn are left-dominant. Middle America is right-dominant.)