Utah’s polygamy law wasn’t really “weakened” by a federal judge
The parties in question never sought legal recognition of their polyamorous relationship from the state. They did not have marriage licenses, for example, with the exception of the husband and his first (and still only legal) wife. The parties did not seek to take advantage of laws that apply only to married couples.
The issue is whether the state could criminally punish married people simply for cohabiting. The court said no, as a matter of constitutional law. The section of the statute criminalizing multiple marriages remains intact.