No.

I have been all over the world, and even as a kid, I was impressed that most cultures really do want the same things...after the basic needs of shelter, food, water, etc., they all want something better for their children...the golden rule seems to also be predominant, though said in different ways...pretty much, people want to be left alone to figure out, in their own way, why they are here and how they can make the best of it...being a human and understanding what that means was often a topic of discussion no matter where I was.

Perennial Philosophy by Aldous Huxley. He argues yes.

They vary depending on culture

Not that exist "out there" for everyone to stub their toe on, exactly, but there are some harms that are so universally clear and present dangers to society that virtually all societies share similar convictions about them. Things like murder outside of the context of war or self defense, child neglect or exploitation, and rape are either universally forbidden or at least those governments who allow them in some form, show consciousness of guilt in doing so, by attempting to hide or cover up such activities, and generally by maintaining a facade of being against them.

Societal morality is all about generally agreed-upon harms and how to discourage them from happening. Some harms are more ambiguous or disputed or depend on how you frame the conversation about it. And what's considered universal today (e.g., slavery is a great harm and a gross violation of civil rights) wasn't accepted at all, say, a couple hundred years ago. Or ... it was only accepted for white people or white men or wealthy white men or whatever, rather than for all.

So morality evolves, too.