If I go to the public library, check out a movie on disc, back it up, and share the back up file online, is my public library legally liable

Depends a bit probably if your local library has major lawsuits for operating in a very sketchy side of the legal gray area

Maybe your library shouldn't have made choices that put it at odds with the data preservation community then.

Strongly agree, but what does that have to do with the point I was making: that yes indeed they might be liable, and are different than a library?