That's just nihilism, if there are "other moralities" that are just as valid and that I can freely choose, there might as well be none.

No moral relativism does not entail moral nihilism. People can have different morals (in fact they do), that doesn't imply that all morals are meaningless.

You can also choose (if you decide you are free to choose) the set of morals that makes you the most happy (hedonism) or give you the most utility. Or you can decide to be a nihilist.

So it's not the same.

That might be true for whatever moral principals you personally choose for yourself, however if I can't hold anyone accountable for immoral behaviour, because they might have just chosen another set of morals for themselves, that's nihilism.

It's not his morality unless he works at Facebook.