For anyone who does not know, Shakespeare does not describe Cleopatra as Hellenistic monarch, instead she is portrayed as a "gypsy" (meaning an Egyptian before it became solely associated with Romani "gypsy" travellers who were mistakenly thought to come from Egypt), of "tawny" (tan) hue, with a breast that "pinches black", and is often considered black in the same sense as Shakespeare's Othello, who is described in similar terms, is "black". Of course, concepts of what made a person "black" were different at the time but I am writing this to ask what contemporaries felt so this is somewhat irrelevant.
Although I have dived into the ramifications of this for changing perceptions of Cleopatra as an Oriental seductress, I never actually gave much thought to how contemporary audiences would have reacted to this.
As /u/cdesmoulins stated here in Was Othello's marriage to Desdemona in Shakespeare's Famous Tragedy a Scandalous or Bold Topic?:
Black people were not exclusively exotics in Elizabethan and Jacobean England; indeed they may have been in the audiences for these plays. But popular stereotypes of blackness were negative and lended themselves to dramatization on the stage anyway -- black characters appeared in Elizabethan and Jacobean drama, and references to black skin pop up with negative connotations to contrast the corresponding idealization of "fair" whiteness. Blackness on the Elizabethan and Jacobean stage is perilously close to devilishness, dirtiness, and difference, not just racially.
But in other respects their [Othello and Desdemona's] respective fates would have played into white audiences' expectations -- that black people are good enough to work alongside but not so good to marry, perhaps, or that black people are unhappily different from white people, for instance, inadvertently reinforcing the prejudice that caused that same unhappiness.
Obviously Antony and Cleopatra's story has to end in tragedy but how did English audiences perceive this (now interracial) relationship and the portrayal of Cleopatra as a whole?
How would Cleopatra (or Othello) have been portrayed in Shakespeare play in Elizabethan times. Would they have found a dark skinned person to play these roles, or would they have used make-up? Would the makeup have been to make a person what we would consider black, or what we would consider middle eastern?