[itsme]

Not showing the filters bar in a setlist is one really good solution.
Another possibility that would be consistent for all tabs would be to have separate filter settings for each of the library tabs, different for Songs, Collections, Setlists and so on. The same filter bar UI of course, just persisting the filter bar settings independently.
The group editor should have its own. One set of filter settings (not caring about the group it is editing) seems enough for me, but it is essential to allow the group editor having different filters than the corresponding group.
For me it would be a helpful use case to apply a well-thought set of filters on "Songs", a different one on "Collections" and none on all other library tabs. Just as an example.
Keeping them when MSP is restarted would be convenient, but not essential.
Storing filter settings per setlist seems too much (for me)  and not required at all.