What does this simple phrase mean?

A woman was faced with a decision she had to make.

No matter what her decision would be, she would definitely upset some people.

So, not having the choice to offend no one, she was actually free to make a decision based on merits alone.

As for other people's reactions, well, that was on them.

It was up to them to decide to get upset over another person's actions, and therefore it was only up to them to get over it.

And if they didn't get over it, well, that was on them.

Another way of saying it is the simple idea that what people think about me is none of my business.

As long as I'm true to myself, I'll be happy with my decisions.

And if someone has a problem with that, well, you know.