Their exemption isn't a privilege that's subject to conditions, or a trade off for political nuetrality like a 501-C. Their tax exempt status is vital to assure that religion and government can't have power and influience over each other, and to assure that the government can't use taxation as a means to abridge freedom of religion...
a) "In God We Trust" was printed on the money being in the 1950's. This motto would not pass the lemon test (government shall not promote any religion).
b) Although it shouldn't be anybody's business, politicians' religious beliefs are put in the spot light. For example, many claimed Obama is a Muslim and didn't want to vote for him because of that. Romney is a Mormon.
c) People are trying to throw out science and teach religion in our public schools. Religion has no place in these schools to brainwash our children. School is for learning and evolution is fact, not creationism or ID.
d) During holidays, there are posted signs of "keep Christ in Christmas" on public/government property. Besides being inaccurate, this will not pass the lemon test.
e) Politicians and others are using their religion as bases for laws such as gay marriage and abortion. No religion should be forced on everybody (freedom of religion).
"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances." --First Amendment to the United States Constitution