The question there ... is ... what governmental agency would then be granted the authority to make a determination on whether something qualifies as a religion?
Then, once you identify that governmental agency that does that ... then where in the US Constitution would grant that authority. Or better yet ... what section of the US Constitution would override the “First Amendment” in our Bill of Rights?
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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.
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The First Amendment (Amendment I) to the United States Constitution prohibits the making of any law respecting an establishment of religion, impeding the free exercise of religion, abridging the freedom of speech, infringing on the freedom of the press, interfering with the right to peaceably assemble or prohibiting the petitioning for a governmental redress of grievances. It was adopted on December 15, 1791, as one of the ten amendments that constitute the Bill of Rights.
This Act does not determine if Islam is a religion. It simply says that Islam does not qualify for tax exemption. This happens all the time.
They can still be a “religion” but we simply would not have to subsidize them with our tax dollars.