Stan loves him...or at least he did before like the shitty 2011+ seasons, and even in the latest stuff he doesn't 'hate' him at all. Also Cartman, though he hates Kyle, is clearly obsessed with him in some other way as well.
Kyle just has this prissy, short-tempered, conscientious, whiny personality that some people find difficult and obnoxious but some people like Stan find very endearing. It's worth noting that both Kyle and Wendy are very similar personality wise and also they're both very academic, they both like to make people think of them as moralfags, and they both hate Cartman. Not a coincidence that Stan really likes both of them.
The same people who hate Kyle are the people who don't 'get' Choromatsu. It's a taste in boys thing