Othello would be so obviously different in his skin color that he would at best arouse interest and curiousity, at worst, the deep prejudices of the more ignorant Venetians. We onlyhave to see the hatred that is shown by Iago to Michael Cassio, condemned for being ' a Florentine'. Florence is a lot less removed than Africa. There was still a suspicion that black people in particular used spells and witchcraft, and indeed Othello is charged with these actions by Brabantio.
As posted above, a Moor was a dark-skinned person. The conflict which could arise from a Moor being in a play was based upon the thoughts about how the Moors were different and, therefore, beneath the other characters.
Yes, the derogative phrase "Moor" is used to indicate Othello's position as a definite outsider and also to point out the threat that he represents to the Christian community. As a Muslim and a black individual, he is "othered" by the majority white Christian community and made into a potential threat.
Iago specifically expresses his hatred of Othello by referring to him as the "Moor" throughout the play, using it as a racial epithet.
The term itself could also have meant a nonwhite not of Spanish or African origin; in Shakespeare's day it could have implied a non-Christian, or a religious outsider.
Back then, the difference in religion was (or maybe was more so) more important than the difference in skin.
The word "Moor" was often used in Shakespeare's age to describe black Africans. it could also be used to describe Muslims. Othello is black, but he is not a Muslim. His blackness (as the play shows) is the object of a great deal of racial prejudice, especially after he secretly weds a white woman. The racial prejudices of Desdemona's father seem to be especially aroused by the interracial marriage of his daughter and Othello.
I'll try and highlight the situation with a modern parallel. The Moors were North African and Spanish Muslims and Othello is the commander-in-chief of the Venetian military.
You ask if Othello's ethnicity and religion might have been a problem for Venetians. Well, look how much fuss and panic people make nowadays at just the suggestion that Obama is a Muslim. And while it is not discussed openly do you think Obama's ethnicity is a problem for some American voters?
In the same way, prejudiced Venetians would have been deeply, deeply suspicious and paranoid about the motivates of a non-white, non-Christian leader fighting the Turks for them. I mean... Venice is at war with The Turks!?! They are at war with non-white, non-christians Muslims like Othello!!!
"OMG! He's one of them!!! Othello will sell us out to his true allies. He's a puppet of The Sultan! He worships their God. He hates us. We're walking into a trap. Wake up, Venetians! Can't you see this guy is the ENEMY? He wants to turn us all into Muslims by force. Check out this 16th-century website! It PROVES there's a Muslim conspiracy!"
and so on. Othello's race and religion would have been a BIG problem for many people.