I think a lot of people will appear to be nihilists or relativists if you ask them about meta-ethics directly, but it's unclear whether that's really a good way to describe them.¹ Most people will struggle to provide an objective basis for their moral views--that shouldn't be surprising, it's the impetus to the entire history of moral philosophy. So when pressed, they say something like, "Well, morality is ultimately subjective, etc."

I'm wary of concluding that people like this are skeptical of objective morality, because they don't actually act or talk like when moral issues arise in everyday life. If you wrong them, they won't accept as justification that morality is illusory, or that your personal values differ from theirs. More likely, they'll react as if there is an objective morality that all of us can reason about.

¹As an aside, I think it's true in general that the best way to assess someone's attitudes or beliefs is often not to ask about them directly. People reveal themselves implicitly, not explicitly.