This is unusual, to say the least:

A Seattle Episcopal priest who claims to be both Christian and Muslim
has been restricted from public ministry and will be defrocked unless
she “reclaims” Christianity by next April, the Episcopal Church
announced.
…
Redding, who teaches at a Jesuit seminary in Seattle, according to
Episcopal News Service, told ENS that “I do not believe the canons were
written with this situation in mind. … My situation gives the church
an opportunity to re-examine what it means to be in communion.”

You know, I have to say I am much more sympathetic to the church here. I agree that Islam and Christianity are very similar in many ways, but the differences in basic doctrine are just too stark – the obvious issue being the status of Jesus AS as prophet or god, and the validity of the whole of the Qur’an as a divine text or not.

I am reminded of the main character in the novel Life of Pi, who embraced Hinduism, Islam, and Christianity all at once as a child growing up in India, triggering an angry confrontation between his three spiritual advisers. It is an incongruous, absurd situation.