Speaking for myself, I've always accepted but disagreed with socially moderate to even liberal Republicans as long as they're with us on other issues. I've also said the same for populist Republicans who aren't always with us on economic issues. Same with those that don't necessarily accept the modern conservative Republican views on foreign/military policy.
That being said, I've encountered plenty of "big tenters" that are socially liberal and want to be personally accepted but want to shut the door on populists.
Hypocrisy has always been a strong suit of supposed "big tent" Republicans who crow about being included, but then demand as a condition the removal of certain "undersirables" they find embarassing to be associated with in their social circles.
Ugh. It's like those homophobic black people who say things like "I fought for my right to fight against other peoples' rights!"