I'm not sure what you're saying here. Are you suggesting moderation of online discussion is coercion, and therefor criminal? I think the entire legal system (US specifically) would disagree. Or are you suggestion that a user that is using coercion is criminal, and something you would put a stop to?

> Should I stoop to the level of a common racist by FORCING him/her to speak a certain way?

That's a judgement call to make, depending the context of the site. Yes, you can make the argument that censorship of hate speech is as unethical as the speech itself. I'm not sure if I agree or disagree, and it's a bit of a rabbit hole. Or you could make the argument that your site is for particular discussion of certain topics, and if it's well known what the rules are, there's great benefit to the community by enforcing them: eg /b/ vs Hacker News.

> I've no right to tell people what they can and can not say

You absolutely do, if they are using a site which you own or are in some way in charge of. The same way you have the right to tell someone to get off your lawn.

> nor will I hold myself responsible for their thoughts and actions. It's their burden to bear.

You don't have to hold yourself responsible, but your users might. And shrugging that responsibility might result in a bad experience for many users, depending on how the culture and discussion of a site develops.

> Should I stoop to the level of a common racist by FORCING him/her to speak a certain way?

You are not a Forum. On the other hand, your comment implies you try to convince someone to act (not) a certain way. The difference between the force and conviction might make all the difference, but conviction is one kind of force, isn't it?