I should have elaborated. I don't plan on watching the physical media. I plan on watching a digital copy of the physical media where the physical media is just my legit license. Obtaining a digital copy of the library's physical media is not something I'd be willing to do.
Why not? Your taxes pay for the library, so you own a share of their media. If you really want to be honest, check their online catalog and make sure the title is available for checkout before you play it.
Speaking as someone who worked at a public library: do it. You paid for the movies and they're provided as a public good. I can guarantee that every single piece of media on the shelf has been ripped multiple times. People do it very frequently.