Tbh, I don’t think anyone in the fandom treats Kyle’s feelings for Cartman well. Like, it’s always to one extreme (kyman) or another (complete hatred) and I don’t think it’s as simple as that.
No one ever considers the fact that Kyle might outwardly say he is not affected by Cartman’s antisemitism but he can actually be filled by a lot of self hatred because of it. I can imagine Kyle growing up and moving to a big city like New York and roll his eyes when the Jewish people in these cities act “too” Jewish, if you will. It’s exactly how he reacts to his cousin Kyle, with annoyance and worry and a desire to not associate with him. This aversion to overly Jewish traits didn’t come out of nowhere, it came because of Cartman. It’s not overt self hatred, but it’s a desire to try to make himself appear as the right kind of Jewish as opposed to the overt kind. This subtle self hatred also appears with his obvious displeasure in his own curly hair, and in The List he was offended when it was implied he had his mother’s (I think it was hers) nose, since she’s drawn with a more prominent (read: Jewish) nose than any of the other adults on the show. He’s offended and hates his own Jewish features. Again, this doesn’t come out of nowhere, this comes out of Cartman chipping away at him for years.
Kyle is definitely someone who also believes he’s above Cartman’s shit, and he would never admit to himself or anyone that any of Cartman’s taunting has affected him in any real or meaningful way. I don’t even think Kyle would acknowledge his aversion to overt Jewish traits as a bad thing, but rather as a measure to blend in that he’s chosen to do on his own. Because of this, I don’t think Kyle would ever truly hate Cartman with such a passion he tries to cut off all contact with him, or whatever the kids head canon these days. I think there have been enough instances where Kyle and Cartman have been able to successfully work together and I think Kyle would value this and value Cartman’s friendship to a certain extent. I personally believe Cartman chills out as he gets older, and in this scenario Kyle would be able to forgive and disregard Cartman’s childhood antisemitism and merely childhood taunts, but the damage has been done and unless Kyle realizes there’s damage in the first place (which I don’t think he would), then he’ll never seek out help or attempt to unlearn his self hatred. (So one could argue that Cartman’s antisemitism is even more insidious since Kyle is being seriously affected, but he’s so use to it he thinks he’s alright.)
Long story short, Cartman and Kyle have a complicated relationship that can’t be boiled down to as love or as hatred, and it’s p boring when people try to simplify it. Cartman is a toxic person for Kyle but Kyle still finds some fruitfulness in their friendship. Ironically Cartman said it best in Casa Bonita, they may not be friends, but they’ve been through a lot together, so that certainly makes them something.
