Another liquid cleanser fan here. It won’t scratch or wear away the surface. A soft sponge is used for the same reason. The key is to do it on a regular basis so there isn’t an opportunity for build-up or mold.
@augustlan: What @ccrow states about your tub is true. There are tubs made out of metal with an enamel finish. Repeated use with a harsh scrubbing agent will eventually wear away the enamel finish, giving the tub surface a dark, dingy color where the metal is exposed.
On the other hand, if the bottom of the tub had a non-slip surface applied at the time of manufacturing, usually in the form of a bunch of coin-sized dots, it could be a cleanliness challenge. The way to tell if it is stained (cleanliness) or discolored (condition) is to feel the tub bottom.
If the applied non-slip surface can still be felt, it is a cleanliness issue. We (hotel inspectors) found that a cleaning product like 409 Orange and a Magic Eraser remove the scum build-up in the crevices. We tried this in several hotels, and it made the tubs look brand new. (I wish I had kept the photos.) If the tub bottom feels smooth, then the non-slip surface has worn away.
Personally, I don’t recommend having the tub resurfaced. After witnessing many hotel tubs that have been resurfaced in various ways, I have yet to see one that doesn’t look odd and holds up. In my book, the charm of a claw-foot tub trumps the dingy appearance.