The difference is that slavery is inherently wrong, whereas deciding on your own internal membership policies for some club, or internet forum, or what have you, is not inherently wrong.
This is pretty obvious, because nobody's mad about the small private actors doing the same kind of thing. 99.9999% of the companies or private groups around, nobody gives a shit that they get to decide to ban whoever they like. They're just mad at Facebook and Twitter because they're big. Whereas "small time slaveowners" are still disgusting criminals.
And I get that, these companies being more powerful, their decisions have wider knock-on effects. But the right solution is still alternatives, not the government micromanaging and second guessing every single decision they make. At most, you could mandate some kind of 'nutrition facts' policy, where policies must at least be up front and transparent.