Sounds like that's their problem to figure out, and I think that's right. I would 1000 times rather have more birds at my feeders than the neighbor's cat pooping in my yard, hunting birds and bothering my dog.
Let them put in a good fence, electric collar, leash with one of those zip line things - whatever they have to do.
At bird feeders the percentage of individual visitors that are non-native is often much higher. The non-natives tend to be more generalist eaters, whereas the native specifies tend to stick more to their native diet which isn't as well served by most feeders.
By drawing in these generalist non-natives feeders tend to actually displace native birds from the surrounding area.
That's why when I was feeding birds I didn't really worry about cats getting into my yard. I couldn't think of a way to make a good argument that the line of how much harm it is OK to do to the native environment for your enjoyment is somewhere between the harm feeding non-native birds does and the harm the neighborhood cats do (especially since I've never seen a cat catch a bird in my yard).