In many ways, yes they should.
First off, freedom of religion only works if it works both ways. When Christian groups are influencing politics with huge amounts of money, then they should have to pay taxes. See for instance the Mormon church's involvement in the campaign for proposition 8. To put it simply, Churches should not be free from government (no taxes) unless government is free from religion.
Another issue is that the classifications for a religion are incredibly vague. John Oliver did a great show about how easy it is to establish yourself as a tax free group which explains the problems with religion when it comes to taxation. https://www.youtube.com/watch?v=7y1xJAVZxXg
I have no problem with church and state being separate. However, when religious groups spend money pushing for religious instruction in schools (intelligent design), spend huge amounts of money to oppose gay marriage, spend money to oppose abortion, and support numerous other causes no support, then there is no reason they should still enjoy the benefits government subsidy.
(http://www.washingtonpost.com/news/wonkblog/wp/2013/08/22/you-give-religions-more-than-82-5-billion-a-year/)







