I know of a convent that operates a soup kitchen - nice people. I would think it appropriate for the soup kitchen to be tax exempt/ have charitable status, but outside of that I can't see why they should have any special status.
And it is not mandated in the Constitution. One argument for exemption is: separation of Church and State. I see that as the opposite; granting favors of no property tax is an involvement. It separates them from everyone else.
As Mark Twain argued: "no church property is taxed and so the infidel and the atheist and the man without religion are taxed to make up the deficit in the public income thus caused." Strangely, this logic seems more sound.
I am joking in part, because the reason for the tax break which started in 1894, was that Churches provided a much needed service. And consensus was to approve of this noble gesture. Today - 118 years later - we have the need to make some changes. True charity is easy to track. And there are some much needed services that some Churches provide. In the South, they have provided for black communities as a tradition. And then there are the other guys.
According to former White House senior policy analyst Jeff Schweitzer, PhD, US churches own $300-$500 billion in untaxed property. New York's nonpartisan Independent Budget Office determined in July 2011, that New York City alone loses $627 million in property tax revenue. Lakewood Church, a "megachurch" in Houston, TX, earns $75 million in annual untaxed revenue, and the Church of Scientology's annual income exceeds $500 million.
I certainly don't want a bunch of politicians deciding what constitutes a valid religion and what doesn't. I fully support a redefinition of what constitutes charity and charitable works, though, and agree churches should only gain tax exemption on things of that nature. That alone would be a game changer IMO.
If it provides a needed service to the community and is done without cost to the recipients then it's charity.
