Honestly yeah, Wendy would not want to deal with Cartman and chooses not to deal with Cartman. I mentioned this before, but everybody in South Park has acknowledged, in The Death of Eric Cartman that ignoring him works. (to an extent. ) The main difference between Wendy and Kyle is that Wendy chooses to ignore him, whereas Kyle does not ignore him. 

And Cartman’s response to Wendy ever speaking seems to be a little more bitter than playful with Kyle’s.

Any time Wendy and Cartman have any kind of debate, Cartman is incredibly dismissive towards Wendy’s arguments. He doesn’t treat them as arguments, he treats them like jokes.

When Cartman and Kyle fight, however, Cartman’s response to a disagreement is either playful teasing or arguing right back with Kyle. His arguing with Kyle is more “bargaining”-esque than his arguing with Wendy, because he’s eager to prove Kyle wrong.

With Wendy he doesn’t have the urge to prove her wrong, he simply automatically asserts that Wendy is wrong, or isn’t to be taken seriously.

That’s not to say that I don’t think Candy isn’t plausible. I’m pretty sure Matt and Trey have mentioned that Cartman did have a crush on Wendy. Though I need to find a reference for that… 

His desire to end arguments quickly with Wendy could just be a way of avoiding direct challenge with her, because she makes him nervous. It’s up for interpretation, as all interactions are.