I think your image of Republican Party messaging is wildly out of sync with how Republican voters see it. It’s closer to where religious faction of the party has been in early 2000s, but it hardly resembles their position today. I do not find it particularly surprising, given that one simply cannot get an accurate view of it without explicitly looking for it: you won’t get it in CNN or MSNBC, and most non-Republicans would never stoop so low to actually watch the “partisan hacks” on Fox.