Both the progressives I know and the conservatives I know are pretty tolerant of dissenting speech in that they disagree with it but don't advocate for it to be silenced.

But at the same time, both the progressives and the conservatives who are active on political social media (take your pick of platform) are very likely to actively attempt to silence the opposition and punish them for speaking.

It's less a political divide and more that most people are still tolerant of dissenting speech, so the people you know in person will tend to be tolerant. There's a loud minority that's vocal on the internet on both sides that advocates for silencing others.

The sense I get is that those on the far right are worse than those on the far left, but those on the moderate left are much worse than those on the moderate right, to the point of being nearly insufferable.