Instead most people seem to believe themselves to be politically rational, and hold that as a very important value (or so I believe).

That depends a bit on the enviroment. There are cases where people care very much of signaling group alliance. On the left you find people competing on being more ideological pure than the next person.

I had one experience with an extremly smart person, which politically influential parents and maybe a future political career on her own who once quite explicetly said, that's what she was doing after she read a room wrongly and excused for that (it wasn't a even a public event but party internal).