Can Othello only be played by a black man now?

With the news that WalterdaleWalterdalr Theatre, a small amateur theatre group in Edmonton, has been browbeaten into cancelling a controversial production of Shakespeare's Othello, the old face-off between artistic freedom / free speech and political correctness raises its head yet again.
The planned production was to be set in "a post-apocalyptic world where traditional power structures were inverted". Not my cup of tea, perhaps, but not immediately controversial - Shakespeare has been played in so many weird and wonderful ways over the centuries, that this is far from the most outrageous.
What has put the cat among the pigeons, though, is that the part of Othello was to have been played by a white person, a female white person at that, in the unfortunate person of local performing arts teacher, Linette J. Smith. Social media, predictably, lit up, and long-time patrons expressed their outrage and dismay, with one particularly menacing message that made Ms. Smith distinctly uncomfortable (although no charges were pressed). And ultimately the production was shelved until cooler heads prevail.
Many complained that the role of Othello is traditionally by a black man - not strictly true, given that the first time a black Canadian played Othello at Straford was only ten years ago, and the idea would.have been unthinkable in Shakespeare's time, or in most of the four centuries since. Yes, we may be more enlightened and less racist nowadays. But does this mean that theatre has to be so hidebound, restrictive and predictable that only a black man is allowed to play Othello? Could an Asian man play him? Could a black woman? Could a black woman play Desdemona? Does the actor playing Shylock need to be Jewish? And if a small provincial amateur company happens not to have a black man willing and able to take the star role, are they allowed to mount the play?
The ever-sanctimonious J. Kelly Nestruck, theatre critic for the Globe and Mail, clearly thinks not, as his smug, preachy article ably demonstrates. Me, as you may have gathered, not so much.