The best Anti-Bellwether?

I posted on the bellwether topic a month ago:

Bellwethers are easily explained: they are states near the “red-blue divide”, so when there’s an overall blue tilt, they go blue and vice versa. “Anti-bellwethers” make much less sense.

Another trivia question with an interesting answer is:
Which state(s) produce the most lop-sided votes in Presidential elections and which Party does it vote for?

The answer, IIRC, is Mississippi (with Miss. geographical neighbors also “scoring high”). Interesting is the answer to the subquestion: Mississippi gave the Demos overwhelming majorities before the Civil Rights Act of 1964 and gave the GOP overwhelming majorities afterward.