One thing I appreciate about grief support groups and 12 step groups is the "express no opinions on outside issues" stance -- based on hard lessons learned. If you are a parent whose child has died, I don't care if you are a Republican, a Democrat, a Maoist or a Randian, you are in pain. The shared pain binds us together, the other matters are not relevant.
It becomes more significant as you cross the country. Arnold, the Governator, was a conservative governor of California who favored gay marriage, was pro-choice on abortion, and raised taxes. Probably opposed the death penalty. In Texas, I've met a lot of Democrats who are pro-life on abortion, oppose gay marriage, are pro-death penalty and want to reduce taxes and regulation.
I've often noticed that many of the liberals I've met in Texas were to the right of the conservatives I knew in California. In California I went to school with Libertarian Marxists, in Texas I've yet to meet any libertarians who encompass Marxism. But then I haven't met any cute Trotskyist Socialists either in Texas.
The LDS Church used to be overwhelmingly Democratic. David O. McKay's sons for example. At least one of his grand daughters I met at BYU as well.
Spencer W. Kimball's book, The Miracle of Forgiveness, had very strong things to say about social equity, e.g. http://timesandseasons.org/index.php/2011/11/a-prophet-occupies-wall-street/ -- things that informed my willingness to volunteer and involve myself in soup kitchens, rape crisis centers, pro bono work and child advocacy centers at various times.
That seems to have changed in some areas, mostly driven by demographics and other issues, as well as by fault line issues. As a result, the LDS Church keeps a couple "officially Democrats" general authorities who are asked to address the Church from time to time on the topic of political neutrality and that there really is not a quasi-official "holy" or "appropriate" political party with all of the truth.
It was hard for Republicans (and still is in some places) in the 1960s and 1970s, it can be hard for Democrats in some areas now (though Harry Reid and others manage just fine).
I think that a church, like a 12 step program, or a grief recovery group, is well served by returning to care for itself and the needs of its members and avoiding embroilment in political discourse that deprives us of the support of each other.
Lest we forget Christ and replace him with someone else.