IIRC, all cheese has mold. Some of the mold is safe and/or desirable to eat (blue cheese's blue is mold).
But those soft cheeses can grow other mold: If it does this, you have to throw it all out as it could be dangerous. In general, you don't want mold where you didn't expect it.
Sorta. Fresh cheeses, like curds or paneer, don't have significant bacteria or mold colonies, outside whatever natural stuff happens to be on all food. All aged cheeses have bacterial colonies, that's what does the aging, fermenting the milk's sugars into acid and other tasty byproducts. Some cheeses have mold as well, but not all. Usually it's on the surface, and breaks down the milk's proteins which turns it soft. That's why when you slice into brie or camembert, the outside is the softest part: the white, fuzzy mold on the outside has done its work on the proteins there. Blue cheese has holes poked in it where they insert the blue mold spores, to more evenly colonize the entire cheese instead of the outside.
Many cheeses actually benefit from acquiring wild mold colonies. There are ways to tell which molds are "good" and which are "bad," which home cheesemakers can learn. Here[1] is a properly aging cheddar, wrapped in bandages and allowed to mold. The mold gives some flavors, but more importantly dries out the cheese's exterior and acts as a guard to prevent nasty bacterial infections from getting into the "good stuff" in the middle.
But those soft cheeses can grow other mold: If it does this, you have to throw it all out as it could be dangerous. In general, you don't want mold where you didn't expect it.