> trying to control others' thoughts isn't going to change that
Controlling the spread of misinformation is not "controlling others thoughts".
> your assumption is that banning free speech would improve things
Banning specific content such as anti-vaxx is not "banning free speech". If anything, let it go rampant on your platform is actually helping promote it. Private platforms have no such obligation. It's like if I came to your house and forced lies about you to your family, and when you threw me out, I claimed that you were trying to ban my free speech.