I don't really think Othello (in Shakespeare's intentions) was about race. You can easily tweak it slightly as such as people have been doing for a long long time yes, and that's cool and even the way it's done all the time. But that just doesn't make much sense given the actual context of the times. Which was a big West Side Story gang war over the Mediterranean between the Khristianz and the Muzlimz. That's the whole setting. Venetians hanging out on eternal army base Cyprus getting ready to kick Ottoman butt (spoiler: Ottomans kick their butts instead). Kyle even showed like a painting at one point of the battle of Lepanto, the ultimate gang rumble of the times.
A dude from Morocco is not going to stand out tremendously in Cyprus, though yeah I suppose compared to the Venetians who make up most of the cast he would.
True Shakespeare wouldn't have been aware of that exactly, but the "this guy looks slightly different than us" would be incidental and not the focus of the difference. The "he's from the other gang" thing would.
The point is he's an Other of some sort. Which is why you can easily make it a race thing for Americans, or a caste thing for Indians. Just like a feud between noble houses can be turned into Ethnic street gangs in NYC easily.
He made the point that Indians made Shakespeare Indian, but the real subtext there is that one of the reasons Shakespeare is so popular and resilient over the years most of the stories have a real universal humanity in them that makes them customizable without the point being lost.
You can even turn Taming of the Shrew feminist by giving Katherina some small gesture of rebellion at the end as has been done.