I should add that to your original post given how obviously pro-business the Republicans were from the 1890s on (with the sole exceptions of TR and Taft) it’s kind of amazing that liberal Republicans managed to limp on into the 60s. I wonder if they maintained some kind of vague lingering hope that they could retake the party and possibly force a realignment where the Democrats would nominate a Dixiecrat in response until 1964 when it must have become obvious they had no future in the party.
I mean, we have posters claim that people are RINOs and DINOs
today, so that still is not entirely gone. With that said, actual "liberal" Republicans - which I am defining as being at least as "left wing" as your average liberal Democrat - were never that large in number in the Twentieth Century. A majority of them were more accurately described as being "liberal"
for a Republican. You can say Willkie is a liberal, but you cannot say he didn't run to FDR's right, for example.