Paul says that eating the Lord's supper in an unworthy manner will bring judgment to whoever does it. But that person isn't saved anyway, so what difference does it make?

Well, I don't agree with that premise: "that person isn't saved anyway."

This question sounds like it is assuming that the judgment that comes when you eat in an unworthy manner is hell, and so the person isn't saved. But in fact, what the text says is that we should try to eat in a worthy manner so that we would not be judged like the world, and before that there's another judgment in which God just takes us out of life so that we won't be judged by the world.

So there's a kind of judgment that is not condemnation on the children of God.

That text in 1 Corinthians 11 says that we will be judged by the Lord so that we won't be condemned with the world. That's the way it goes. Judged by the Lord so that we won't be condemned with the world. And one of the judgments is death! He takes the lives of Christians so that they won't go to hell. It's absolutely astonishing! People should read the text near the end of 1 Corinthians 11.

So, no, the person can be saved, can be born again, and still eat the supper of the Lord unworthily. Which I think would mean that he has become temporarily cavalier. He's not thinking about crucifying himself. He's not thinking about forsaking sin. He has fallen into a lukewarm frame of mind. And he's just casually taking these holy elements in some kind of distorted way to think they might do him some good, when what he really needs to do is fight the fight of faith.

Now that is a huge unworthiness that he needs to be convicted about, repent of, and then eat the Lord's supper rightly.