Is Sufism part of Islam, or separate from it?

It is part of Islam, its inner aspect. To claim Sufism is outside Islam is to take the soul out of our religion.

There is a hype in our times that Tasawwuf is not an Islamic discipline or is isolated from Islam. Tasawwuf is the spiritual, inner aspect of Islam itself, cultivating the human’s direct relationship with his Creator, which is the breath and life of religion. [Keller, Sea without Shore]

Fake and worldly “Sufis” have brought disrepute to the word, and that is real. But disease does not prove the non-existence of health. One incompetent doctor does not make the whole profession untrustworthy; likewise, there is good and bad among Sufis.