Naturalism Vs. Supernaturalism (can they coexist peacefully?)

I don't believe there is much hope for these two sides to coexist peacefully. Naturalism involves looking to the world we live in for answers, found in the form of empirical evidence. Supernaturalism involves finding answers to the same questions by trying to look outside our world, or by believing that we already know what is happening outside of this world through "faith". Since the questions often raised for these two sides to answer in the form of culture wars are incredibly important ones, and because they are such a contrast against each other, it doesn't seem likely that they will ever be able to agree on anything. The two ideologies can exist peacefully, as long as they are kept away from each other. When you mix, for instance, a group of people who believe that they are carrying out God's will by demonizing homosexual relations, and a group of people who believe in free choice and the ability to rightfully love someone of the same sex, especially ones making this decision after viewing the world around them and finding no evidence of harm done to anyone, you then have two very different groups arguing about a very important topic that cannot find a neutral ground. They will continue to disagree because of the basic approaches they take towards justifying one side over the other, and there will be strife between the two sides.
The only real way I see for peaceful coexistence to happen is for the two sides to stop arguing, and for public policy to be mandated only through this-world empirical evidence. If all we can agree on is this-world, then that is how we should decide things. This may seem unfair, but there seems to be no better way to proceed. The two sides will speak with mutual respect to each other, Supernaturalists will have to find a way to justify their arguments using empirical evidence (otherwise there is no reason they should expect a naturalist to believe them), and eventually, humanity will decide for itself which sides serves it better. One side will continually disprove and shine doubt on the other, and we will someday know for sure how we will truly be better off.

1. Is there a possibility for a neutral, respectful environment in which Naturalists and Supernaturalists can debate, while both feeling as though they are respected and their ideas are being given a fair evaluation?