Yes, polygamy is illegal, but only when you are legally married to more than one person. What constitutes being married, a legal document, or a promise? I doubt if the FLDS men were legally married to more than one woman. It’s not illegal to live with a woman or women without the benefit of legal marriage and it is not illegal to father a chidren by women that you are not legally married to.
In Texas it is considered Bigamy if you are legally married to one person and you are living with another under circumstances that would lead anyone else to believe that you are married.
So if any of these men were legally married to any other woman, and then lived with another person under the appearance of being married then they have committed bigamy.
While Bigamy is a misdemeanor, conspiracy to commit a misdemeanor is a felony. Since the FLDS Church officials purport to marry these people knowing that they are going to be committing bigamy, you have a conspiracy to commit a misdemeanor and hence these guys can be prosecuted as felons.