Are Sufis Muslim?
As you already stated, we have no right to call anyone a Non-Muslim who himself claims to be a Muslim. Ghamidi sahab has explained that he calls tassawuf a parallel system based on the writings of Sufi scholars. For details please watch: https://youtu.be/s9Z-T9ZHfos?si=bqfzOA1LcCcYfn48
We have no right to accept or reject. We call them whatever they call themselves.