"Relate" means to understand and like or have sympathy for someone or something. It's not wrong (although it would be "relate to [someone]", not "relate with"), but it didn't sound like that is what you meant in this case. You can know someone personally and not relate to them. In this case you wanted to make it clear that you don't know the guy personally, and therefore "associate with" (which means to be in the company of someone, which you would need to do if you knew them personally) would be the better choice.
"I don't understand why my dad is such good friends with that guy. I just can't relate to him at all."
For the second part of the sentence, I think "that kind of person" is best because you are contrasting with a single person (specifically the guy your dad knows but you do not). It sounds a little weird to me to talk about him as "people". I also think it is a little more sharp (critical or harsh) which I think works well in this sentence. You could also say something like "I don't associate with the likes of him."
If you prefer to stick with people, then your original is fine.