Since islam is not a religion (a view which I’ve long held), but rather a political system, it is not subject to the Constitutional protections extended to religions and thus could be subject to laws outlawing it.
Stalin and Hitler both missed a bet. If only they had identified their practices as religion, they might have found protection under our First Amendment.
Where is it written in the Constitution that if a religion has political aspects it ceases to be a religion?
Mormonism in its early years was a totalitarian religious/political system every bit as much as Islam was/is. The medieval Catholic Church was also a monolithic religious/cultural/political system. No dissent allowed. Were neither 19th century Mormonism nor medieval Catholicism religions?
The BIG problem with your idea is that it would require giving a government agency the power to decide which groups are and are not religions. This is a BAD IDEA.
Not unless you're willing to do away with the parts of the First Amendment guaranteeing freedom of speech and freedom of assembly. It would certainly be protected by those.