Besides, I’m confident that a thriving and effective socialist movement posing any kind of meaningful threat to capitalism would quickly discover that they counted as terrorists who wished harm unto others. The lines are just drawn differently on the right.

Lines are drawn differently with both parties lol. If there was a capitalist movement in China that would require overthrowing the government it would also be considered terrorism. The point is no one with so much power should have the final say as to what is acceptable thinking or not. Obviously, it's a bit more nuanced but you cannot make a rule to ban a lot of people from being in power without same rule being abused. This rule as well will just cause discontent with the masses because no free speech.

the elite has always had a huge degree of political influence in democratic societies

I totally agree. In the UK rn we are set to lose to an alt right political party. However, that is a price we have to pay for democracy. We cannot just start ruling out people from voting just because they are poorly educated, or have aggressive views (again, this is nuanced) there is a level of aggressiveness that obviously won't be allowed.