Toilets, Sinks, Showers, Tubs and Disposals - mystery white film in tub (not lime or soap)

This is my infamous 2nd floor bathroom. (To top it off, the fixtures are olive green. :eek:)

Here's my second problem: At the front of the tub, there is always what looks like a white film. I don't think it's lime and I know it's not soap scum. I've tried using Barkeep's Friend and other lime removers and it doesn't budge. If I run my nail over it, it feels almost like the surface has been "roughed up" as if with sandpaper. It wasn't like this when we moved in, and my husband, who uses this bathroom, isn't doing anything that might scratch the tub to this extent.

The net result is that the tub always looks dirty, because while it looks fine when wet, as soon as it dries, the scratches show up and look like white film.

Is ther any way to polish this up? The rest of the tub is in fine shape, it's just on the front wall and rim by the faucets and drain.

It's probably calcium from hard water.
Try CLR or a wet pumice stone to clean it off.
Good Luck!
Mike