One of the problems in legalizing polygamy is that would please the Muslims & their desire for Sharia Law. I could tolerate polygamy if polyandry was allowed also. I would worry, though, that legalization would promote more abuse of women in the FLDS.
One of the benefits about basing your thinking, philosophy and advocacy on fundamental principles is that you need not be concerned about who favors or does not favor a given policy. The policy can be evaluated on its own merits without need to be concerned with who favors it or does not favor it. I would be fairly confident that most Muslims support the notion of brushing one’s teeth before going to bed in the evening. Does this imply that brushing one’s teeth before going to bed in the evening is bad, because Muslims favor it? To me, it is not relevant to the evaluation of a policy whether or not one group or another group favors it. What is relevant is the inherent merits or lack of merit of the policy itself. Besides a person or group can change its mind— and if it does, that leaves you with a problem since you need to reevaluate your assessment of the policy based on the change in thinking of others. That is a form of moral relativism, and as I hope most of us on FR agree, moral relativism is a thing to be avoided.