The question is "who do you want to be your consumers" here. Both choices are PR choices. Legally, you're allowed to do either ("neutral platform" and "moderated discourse forum" are both things that are legally allowed to exist in the US at least).

If you want to appease the free speech crowd, you let the anti-vaxers stay (Gratz, you're running a Chan!) If you want to appease the intelligent discourse crowd, you ban/moderate people who violate your TOS (Gratz, you're running something closer to Hacker News!)