Yes, but not just for relgion. Anyone should be able to live their life as long as it doesn't harm anyone else. If someone wants to pursue a polygamous relationship then that is up to them. As long as everyone involved in the relationship is aware and okay with the arrangement, then I see no reason for it to be illegal.
I believe that polygamy should be a right. After all, why should the government be allowed to tell a consenting adult that he cannot more two or more consenting adults? If a man wants to marry two or more women, or if a woman wants to marry two or more men, it should be allowed.
But as far as the question itself goes, I do not believe it should only be for religious purposes. After all, couldn't anyone applying to marry a second wife simply lie and say they're Mormon even if they're not?
Some religions (even Christianity) allow polygamy, so why should the state interfere? To be honest, I do *not* want a second wife and I recognize that there may be valid reasons for the state to have restrictions that do not match any specific religion.
That said, I am very curious to hear from other Christians who might be able to explain why so many people insist that the Bible says "marriage is between one man and one woman," but my copy only says a king should not have "too many wives" and a deacon should be a man with "only one wife" (implying that other members of the church might have more than one wife).