There seems to be misunderstandings about what Sufism is. Let us start with two terms. Sufism is really a British Orientalist term coined to create an artificial divide between what they found attractive in Islamic civilization (such as Islamic Spirituality) and the negative stereotypes that were present in Britain about Islam. This is a divide that didn’t exist before, but it has continued to the present in the Western world.
The term Muslims have used is Tasawwuf. This has been used to identify the practices of Sufis. Tasawwuf is considered by most scholars of Islam to be merely the name for the inner or esoteric aspect of Islam that is supported by outward or public practices of Islam (i.e., Islamic law). The view here is that it is absolutely necessary to be a Muslim in order to be a Sufi proper, because without the Muslim affiliation, Sufism’s methods would not work. According to Orthodox views of Islam, Sufism is unique to Islam. Take, for example, what happens when neo-Sufis try to showcase Sufism as being universal in nature, its roots predating the rise of Islam and Christianity, which means non-Muslims can then follow the Sufi path with guidance; such guidance and admittance of non-Muslims to the fold of Sufism is considered to be outside of Islamic practices and therefore not acceptable to Muslims.