It is funny how the folks who are most concerned about gay marriage leading to polygamy are the same folks that promote this supposed word of God that condones polygamy.
Re: I've never really got my head round the objections
You answered your own question, and this is it:
"Or is it simply that they feel anything non-Christian should be illegal?"
Fundy Christians believe that anyone who doesn't believe as they do are going to Hell. Even they cannot explain why other "sins," such as fornication are more acceptable to them though.