It does not. It says:
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.
Giving aid to a religion, which would necessarily come by way of congressional action (FEMA's funding and authority is controlled by Congress), amounts to assisting in its establishment.
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And refusing to give aid to a non-profit organization BECAUSE IT IS RELIGIOUS is establishing a religion, of sorts. It's establishing 'no religions allowed,' which results in the default atheist position...or at least an 'anti-religion' position, and that has historically been a very bad idea indeed.
the government should, in fact, pretend that religion simply doesn't matter. That is, if a non-profit organization exists, it shouldn't matter what it is based upon for the purposes of getting aid.
I remember a court case several years ago in Utah. It seems that a school would open its classrooms, after school hours, to student clubs. The only requirements were that the clubs be formed and run by the students, and have one volunteer faculty advisor who kept tabs on the meeting times and makes sure nobody brought drugs and had orgies. Other than that, the school wasn't involved in any of them.
There were all sorts of clubs; LBTG clubs, language clubs (French, German, what have you), chess, debate...even a white supremacist group that met the day after a 'black power' group met. I understand that this was interesting for their advisors..
However, an atheist group sued the school when a 'Christian Bible Study" group wanted to meet. the school caved; because it was a religious group, it was denied permission to meet in the facility.
Luckily that case was kicked up into a higher court, where the judges said that as long as the club abided by all the rules, and as long as the school allowed OTHER controversial groups to meet, they could not deny this Bible study club the right to meet, because doing so was denying those student's freedom of speech and of religion. Big no-no.
As soon as you let religion in as part of the decision making, you ARE establishing a religion and interfering with the freedom of it...and don't kid yourself; right now the politically correct are having their way (and to me, 'politically correct' is NOT a compliment) but what if the tables turn and some religious group takes the new rules and turns them on their head...against non-believers?
Happens all the time.