The key is social conservatism.
Well, just to clarify, I THINK I used the phrase "social conservativism" to describe the agrarian populists like John Bracken, not to describe Red Tories per se. The word "progressive" entered the party's nomenclature because of Bracken, but has not since then continued to describe, neccessarily, the views of people called Red Tories, except in the sense that "progressive" is used to mean "left wing" in countless other contexts.
It is true that old-style Red Tories like Diefenbaker and his academic apologist George Grant took a dim view of social liberalism, opposing things like the legalization of homosexuality and abortion. By the time I was paying attention to politics in the early 80s, however, Red Tory basically meant "left-leaning Tory", and "left-leaning" usually included social liberalism. John Crosbie had been regarded as a left-leaning Tory from way back, and when he as Justice Minister in the 1980s implemented human-rights protection for gays, this was attributed by some to his being a "Red Tory", even though the earlier generation of Red Tories(eg. Diefenbaker and Grant) would have been appalled.
So yeah, in its original usage, "Red Tory" would probably be closer to people like New Deal Dixecrats, minus the racism(and yes, Dief's support was more rural than urban). In the Clark and Mulroney eras, it might have included people who were both economically and socially left-leaning, so closer to Rockefeller Republicans. Nowadays, it basically means "economically neo-liberal, socially liberal".