I'd suggest Super Chix, but they are only slightly less Republican than Chick-fil-a, which is in turn actually less right wing than....drum roll please....Applebee's.
Only a handful of chains actually lean left, Starbucks (just don't even think of unionizing), Chipotle, and perhaps the only "both sides" brand (as in donating equally to both sides), Dunkin Donuts.