These two statements are contrary to each other.
No, they're not contrary to each other. A man can shack up with as many women as he likes, there is no need for any religious or civil recognition of it.
Wyoming, Nebraska, Arkansas, Mississippi, Alabama, Florida, North Carolina, Virginia, West Virginia, and Massachusetts. They're the dark red ones on this map:
Wrong. Those are states which criminalise polygamy, not cohabitation.
A fine, imprisonment, or both
Wrong again. No state in the US fines or imprisons cohabiting couples. The link you provided deals with punishments for bigamy/polygamy, not cohabitation.