A Republican who towed the party line mostly because of civil rights but was out of the mainstream in his party when it came to fiscal policies and foreign policy. By 1912, he no longer felt at home, and the GOP was no longer sufficiently pro-civil rights to keep him.
I can see this.
I just realized Mark Twain would probably be this had he lived a little longer.
Maybe an anti-imperialist progressive Republican who would be inclined to vote for TR but was turned off by his jingoism also.
In past "who would you have voted for" games this is often how i've imagined my voting shift.