How do we find middle ground?

We are so deeply polarized as a people.  How do we re-establish relationship with those who think it's okay to imprison children, who are afraid of Muslims, and who think that poor people are taking their hard-earned cash.  (It's not clear how illegal migrants can simultaneously be taking all those farm jobs that people want, and sitting around on welfare rolls for which they aren't eligible.)

Let's take same sex marriage as an example.  As the Evangelical leaders fulminate about Chik-fil-A deciding to stop donating to the anti-gay groups, how do we honestly come to a middle ground?

if someone tells me that they do not approve of my marriage to another woman, and/or that they approve of legal discrimination, I experience that as deeply painful, personal, and dehumanizing. I understand that they equally deeply feel that my marriage is wrong and against their own values.  But I'm not telling them that THEY can't marry.  I'm not directly interfering in THEIR lives. 

How do you find a resolution between those viewpoints, beyond acknowledging they both exist? 

There's a difference between using your viewpoint to exclude other people from participation, and choosing to exclude yourself. It's the live and let live doctrine. if you don't like same sex marriage, don't enter into a same sex marriage. But don't impose your attitude on others who disagree.

There really isn't a compromise between the view that gay people shouldn't marry, and that gay peopleshould have full civil rights.

Okay, generally, if someone doesn't want to "participate" in a same sex marriage (vendor),well I don't think I'd want them anyway. But follow it to the extreme expressed in Washington State during the marriage battles a few years back:

""What are rural gays supposed to do if the only gas station or grocery store for miles won't sell them gas and food?" The staffer, who refused to identify himself, reportedly told Castro that if such a scenario were to unfold, "gay people can just grow their own food." [Needless to say, the bill did not pass....and the staffer backtracked.]" 

And in the current climate, hate crimes and threats against the LGBT community are rising.

How do I find a middle ground with a person who thinks I shouldn't exist?