What perspective did you expect an English dude in the 1930s have, if not Eurocentric? Of course his fantasy universe will revolve around what he knows and everything outside of that is considered "exotic" or dangerous.

Easterlings and corsairs being mostly from the east, are outsiders and look different, so they fit the bill of being antagonists to his Euro good guys. They also look very distinct in their aesthetic and aren't just another version of Eurocucks in different medieval armor. Would be very boring fantasy otherwise. Literally everything in fantasy is divided among racial and land lines, because that's the easiest way to create conflict. Also, weren't Easterlings just another group of humans that just happen to have beef with middle earth? I don't remember it being implied that they were "evil", just that they were against middle earthers and took the whole "enemy of my enemy is my friend". Probably inspired by the Persian empire that tried to conquer the world.

The average person 80 years ago didn't have the luxury of multiculturalism back then, most people aren't even aware of their own biases in the current century. It's completely pointless to judge a man of the past by the moral standards of today. What purpose does it serve? Even if it was more explicit that he somehow hated black people, would it matter? Do we change the color of "evil" beings and creatures in every fantasy thing, because dark skinned being protagonists is problematic? Do we rewrite the books? He's dead, we will never know for sure if he was actually a racist or not.

I don't remember anyone becoming a radical hater of "dark skinned men" because of lord of the rings.