The popcorn ceilings were original often asbestos. In the mid '70's, they stopped using asbestos. It is a fire retardent, so it had reasons. Later the issues with asbestos fibers became apparent.

A couple things...first IF the asbestos is intact, then it is safe. If it is peeling or flaking off (kids with projectiles aren't good), then it may be better to do something about it.

Secondly, there are laws about the removal of asbestos. By taking it off the ceiling, it gets disturbed. NOT good. There are laws about having a certified company remove it so that the fibers don't get stirred about. It is actually illegal from what I read to remove it yourself. And hey, removing it disturbs those fibers, and you would be breathing it.

If the popcorn finish is removed, then there are disclosure laws about telling buyers of the home.

Do some research to verify the above as laws change.

There are tests to see if the finish is asbestos. You may be past when they sold the popcorn, but sometimes people had surplus and continued after the date of sale.