Those characters span the range of comic books, but, yeah, some of them are from the 60s (or nearby).
Egg Fu is not just racist – it’s also one of the most stupid villains ever introduced. I was embarrassed for Wonder Woman when the character first appeared, thinking “This is just too dumb to be believed” . Having him (it?) talk in that l-in-place-of-r racist dialect just put it over the top.
The Mandarin was Iron Man’s chief Bad Guy for a long time. He’s sort of Fu Manchu as a more hands-on supervillain, but I submit that his chief offenses (as a stereotype, not as a supervillain) were being Chinese and using the name “Mandarin” . He wasn’t originally a martial artist, and his ten power rings came from a crashed alien space ship* I don’t recall them using any other stereotypes in his background. If he’d been a guy named Fred who found the rings aboard a space ship that crashed in Schenectady he wouldn’t even be listed here.
The Ancient One – well, yeah, he’s a walking (or levitating) stereotype. “Eastern Mystic Master” as a spiritual guru from whom you could learn esoteric knowledge not available elsewhere was a trope long before comic books. look at Helena Blavatsky and the Theosophists. L. ron Hubbard claimed to have learned from Tibetan mystics. Dr. Doom retreated to the Himalayas and forged his Darth Vader-inspiring armor among a bunch of monks there. At least it’s not a negative stereotype. Which I admit, doesn’t excuse it.
Luke Cage ( and Black Mariah) – Yeah, he came around as a result of blaxploitation movies like Shaft. No argument there. The problem was that you had a bunch of white comic book creators trying to figure out what to do with the character and have him still be credible 9at least as credible as comic book characters are). If you want another example of this, have a look at the issues of Black Panther that Jack Kirby wrote and drew in the 1970s. It’s a good thing that te-Nehisi Coates later wrote the character.
*Where would super-heroes and -villains be without fortuitous alien spaceships? That’s where Hal Jordan got his power ring, the Mandarin got his TEN power rings, and a lot of villains in the MCU – like the Vulture – get theirs.