But isn't that basically well, "the left" (with all its nuances)

Globally in English I think "liberal" mostly refers more to the economic policy of letting companies do what they want without regulation, which is a right wing policy. Some people take a harder line on this and say that anyone in support of capitalism at all, even with strong social programs in place (like what you might find in countries like Sweden (or Denmark?)) is a right wing position, and you need to be in favor of communism or socialism (or maybe certain flavors of anarchy) to be considered left.

I was wondering if the comment above was just making a classic right wing point

In terms of social issues, I don't really know if it's unique to the US, but there's a tendency in the states in (socially) liberal circles to have sort of "purity tests" in order to fit in. Like if you support most liberal issues like LGBT+ rights, pro-abortion, etc, but maybe you have one issue that you're not firmly on the left about. Say you don't agree that situation X counts as cultural appropriation, you might find yourself ostracized from a particular liberal group because you're not "pure" enough to count as liberal, even if almost all your positions line up otherwise.

Depending on the maturity and life experience of the group and also how non-liberal your position is the acceptance into the group can vary. But these types of policy "checks" are stereotypically more important in liberal circles than conservative ones. However, I admit to not having much experience with what passes for regular (as in, non-government) conservatives, so it might end up being somewhat similar in certain cases. Like if you're generally ok with LGBT issues maybe hardcore Christian groups might not accept you, even if you're anti-abortion.