On January 29th of 2013 The Church of Jesus Christ of Latter Day Saints (The Mormons) filed an amicus brief. against Marriage Equality or Gay Marriage with the Supreme Court.
Said Brief:
http://www.americanbar.org/content/dam/aba/publications/supreme_court_pr...
This is a clear and blatant political stance being taken by a religious (non-profit) organization. This means that the LDS Church is embarking on political endeavor to force the nation to abide by their religion via political means, and that is a clear violation of everyone's 1st Amendment rights.
For this reason, the LDS Church should not be tax exempt.