A Bleg Answered
Yes, two individuals have been fired for being too anti-Muslim:
Ann Coulter was not only fired after an anti-Muslim rant she was fired by a conservative publication, National Review; and radio talk maven Michael Graham lost his job at an ABC affiliate in DC after Muslim American pressure.
Of course, Coulter lost nothing by being cast out of NRO career-wise, but the point stands, especially with Graham. But both said things far beyond Octavia Nasr's artless tweet - subsequently explained.