I can't imagine the round ones and square ones are actually made of different materials. That would be just plain weird.
I've heard of problems with black and brown Bumpons, but have never actually seen the problem. I've never heard of white Bumpons.
I use the clear. Jim Miller offered a great tip about putting a little square of clear framer's tape, or equivalent, on the corners before you put the Bumpons on. This really does help keep them from getting knocked off.
Melty Bumpons must be the asbestos of the framing world. I can visualize teams of highly-trained technicians going around the country replacing Bumpons before it's too late and cleaning walls when it already is.