I get why people have this notion that every Cartman ship would abusive because of the way he treated Heidi, but Cartman canonically has different dynamics with other characters (e.g. Kyle and Wendy are able to put Cartman in his place, Kenny is Cartman’s best friend, Cartman tolerates Stan, etc).

Also, even though there’s proof of Cartman being abusive, there’s also proof in the show that character dynamics can change once there are romantic mutual feelings. People shipped creek before the Tweek x Craig ep because of the toxic yaoi trope, but when they became canon, they’re literally the healthiest couple in the whole show.

So realistically, we will never know how Cartman would be in a romantic relationship with other characters because their dynamic with him are very different compared to his dynamic with Heidi.

Also, a big evidence in the show is that his long term relationship with Yentl is proof that he IS capable of being in a relationship and genuinely loving someone.