They were Some men are described in Tolkien as "swarthy" and perhaps "slant-eyed" as you say, but those are physical traits, not racist. If you were to describe someone as having a slanted eye to a sketch artist, their eye would be drawn at an angle. To not describe it as such when it was physically slanted would be to lie.
If you are offended by physical traits and descriptions of people, that's a you thing.
Easterlings are not enemies of the west because of their skin color or eye angles. They are enemies of the west because they choose to go to war on the side of Sauron, who promises them things in return. Namely to rule oppressively over those in the west, after Sauron's pattern. Likewise, he promises the southern kingdoms the same- free stuff. Probably land, gold, and slaves.
Orcs were bred, likely from elves as one part of their genetics, since they live indefinitely. They are dark because of how they were bred, not because of some perceived racism.
At some point you have to understand the differences between character and colors. Causes and coincidences. Orcs/goblins are dark in character and some happen to be dark skinned. They produce nothing and grow nothing. They were bred for dark purposes and will consume their own just as Sauron and his master consume everything.
The Haradrim and Easterlings (like some of the men of Bree, Dale, Gondor, and as the men who once refused to come to Gondors aid as pledged) simply chose the side they thought would win the war and bring them abundance. Whatever their skin color, the story is about honor and character, choosing good things over evil. Gondor didn't choose to go to war with Sauron or the other kingdoms, nor did they provoke it when peace could easily have been had.
If the pattern of Tolkien, taken from the dispersement of people in the real world, is offensive to anyone, it's just revealing the darkness and/or ignorance in the people reading it.