Non-catholics rhymes with:
catholics, catholics, catholics, acrylics, alcoholics, alix, calix, calyx, catholics, cowlicks, ehrlich's, felix, fralix, gunlicks, helix, hydraulics, interpublic's, italics, metallic's, public's, publics, publix, relics, republic's, republics, symbolics, wallich's, workaholics
Non-catholics sounds like:
nestle's, nestles, newcastle's, nextel's, non-catholic, nostalgia, nostalgic