That’s a good point but Cheney is still more GOPe than not. IMO And I hate to say that because I like him.
He was part of the Nixon admin. whom liberals and weenie pubbies hated!
The vaunted GOP put Eisenhower into office and tossed conservatives Nixon, who wasn't conservative much but was anti-Communist, anti-crime mostly in inner cities (brought mostly by blacks in the '60s), anti-drugs and anti-illegals, whom he knew were carrying the drugs from Mexico, so he wanted them OUT of the U.S.
Libs especially but also the "establishment party" inside DC, loathed Nixon, he wasn't one of "them," wasn't Ivy League, was from a poor Quaker family in a poor CA neighborhood, hated Communism and couldn't be blackmailed - he was one tough guy and fought like a junkyard dog! He brought a bunch of guys like him to run his White House, when he was finally elected. Sheriff Joe became part of that group, that's why he's hated so much.
Cheney became part of Nixon's eventual admin and like Nixon, wasn't one of the "establishment party," he wasn't from the right part of the country, wasn't Ivy League, went to a "nothing school" and married his "nothing high school" sweetheart not a beautiful girl from the "right background who went to the right school, then his biggest blot of all, he was selected by Nixon to come on board with him and became part of that group of guys who never were part of the DC limp wristed gang and Cheney was only permitted on the outer fringes of their cocktail parties.
He will never truly be one of them - and doesn't want to be!
I don't agree him on everything as he's much more liberal on social issues than I am but don't think for one minute that the Bush's and other "establishment" class consider him one of "their guys."