In this article from the IRS website, I learned:
"The IRS has published Revenue Ruling 2007-41, which outlines how churches, and all 501(c)(3) organizations, can stay within the law regarding the ban on political activity. Also, the ban by Congress is on political campaign activity regarding a candidate; churches and other 501(c)(3) organizations can engage in a limited amount of lobbying (including ballot measures) and advocate for or against issues that are in the political arena. The IRS also has provided guidance regarding the difference between advocating for a candidate and advocating for legislation. See political and lobbying activities."
This article proposes that we try to revoke the LDS Church's 501c3 status! They have a good point. As a non-profit organization, you are not supposed to create propaganda to influence legislation. The Mormon Church spent $25 million dollars in support of California's Proposition 8 to ban same-sex marriage. How can they get away with that?
Here is a Petition to Change the Tax-code and Challenge The Church of Jesus Christ of Latter-day Saints’ Tax-exempt Status
Mormons For Proposition 8
Letter from the Mormon Church to its members
Another article here