As a general statement, nowadays states don't care WHO you live with or WHAT you call each other. They care about their own exposure.
If you have registered marriages with two at the same time and die intestate, how do they handle inheritance? Big mess, as estate law isn' set up to figure it out.
If you have two registered marriages without telling each about the other, can one claim that fraud is taking place?
Is your family scamming the welfare system?
These are there true issues.
Within the last 10 years, I know of one state that placed children in a PM home for either foster care or adoption, sorry don't remember which, although in their state even ADVOCATING PM is technically a felony. Go figure.
And over a decade ago, the US Supreme Court took cognizance of the fact that if anyone brought the issue to court, they'd have to take a long hard look at the issue, unless somehoe gays had more intrinsic human rights than do plygamists.
Note that in Texas, the government had to give ALL the kids BACK, even though there was no dispute about them being PM homes.
So I wouldn't give much worry to the states just now.