Is exposed insulation in a basement dangerous?

What kind?

Friable Asbestos? Yes.

Non-friable Asbestos? Not so much, but still not great.

Vermiculite? It may or may not contain asbestos.

Fiberglass? Mice love it, and it can make dust, and it only really insulates if it's completely encapsulated by wall, stopping air movement.

Foam? It's combustible, and current thinking is that it should be covered by a 15 minute smoke barrier. (If there's a fire, you have 15 minutes to get out before it produces toxic smoke.) There are expensive paints that can do this, or you can cover it with sheetrock.