Follow-up: Some readers don't think hunting is a good measure of masculinity. Let's use whether or not a person owns a handgun since it is less rural than hunting.
Logistics regression coefficients (N = 3,833)
Owns a handgun -.395
Belief in God -.363
Conservative politics -.448
All are significant at the .01 level. Possession of a handgun predicts opposing gay marriage, independent of these other factors.