I know a few librarians and I've talked to a few about this before. I have about 12 library cards including my own local district (mainly because my own state has a lot of districts that provide cards to residents of the entire state instead of exclusively locals for some reason. Apparently I qualify for more if I go in person to the specific libraries as well, which is insane to me.) and I did feel guilty for a time about it even within my own local libraries for using it via Libby primarily.

They all told me the nearly same: librarians want you to use their services. Nearly any library service used tends to boost their numbers and provides justification for continued funding. Prioritize your local library if possible, but using libraries with non residents isn't stealing from the locals, its boosting their usage numbers depending on where the district is located. If it's truly a problem and the local residents are experiencing too long wait times, then they will take action (like brooklyn public library did) but otherwise if they offer non residents card, they do so because they WANT people to use them. It benefits them and they have the space to allow the non-residents access, otherwise they wouldn't be offering it as an option in the first place.

Please just use the library in general, anything that makes you use it more, especially locally is a very good thing. It's important to note that in the US, most people do qualify for more than one library card and genuinely don't realize that fact. I was shocked when I learned I qualified for as much as I do when I dug deep enough.