_That_ is what makes his loyalty just barely suspect -- just suspect enough to have him living on edge, and to allow Iago to stab him in the back. The play says nothing about his race, one way or another; early performances could go either way, sometimes casting Othello as black, sometimes as white (if Arabs are white) -- a "black Moor" and "tawny Moor" respectively.
In the present day and age, with multiple half-revived Islamic Ummahs actively at war with each other, and with the loyalties of Muslims in the US military sometimes suspect (cf. the Fort Hood shooting, and a similar active-shooter incident that occurred during the 2003 invasion of Iraq), it says something unflattering about the theatrical world that every performance of _Othello_ is about race, and none about religion.
...
And if I'd read the article, I would have discovered that it talks about precisely that. It mentions that a king from the Maghreb came to London in 1600, and probably inspired the play...
Act 1, Scene 1
Iago: Even now, now, very now, an old black ram Is tupping your white ewe. Arise, arise! Awake the snorting citizens with the bell, Or else the devil will make a grandsire of you. Arise, I say!