[So was slavery acceptable in biblical times and then become immoral in modern times? Whatever is going on, it doesn't sound like an immutable unchanging morality.]

You're an idiot.

Slavery, in and of itself, is not immoral. Kidnapping is. The slavery in the Bible was voluntary. Except in the cases of indentured servitude that were results of the servant stealing [they became servants in order to pay restitution].

The slavery we had in the States was immoral because people were being kidnapped from their homes and forced into it. They did not go into it voluntarily.

And the way many of them were treated was also immoral. The Bible gave guidelines of how to treat slaves and servants properly.