Kids at that age often form their political opinions via positive feedback mechanisms and living up to some platonic Ideal. CC views being Conservative as The Ideal and so he strives to be the most conservative he possibly can be. At that age, especially for precocious youth, sometimes other people (especially far off Turks) seem more like abstractions than "real people". I assume if CC were to really think about it on an intellectual, moral level he would reconsider his plans for Byzantium.
Indeed it speaks to the toxifying impact of Trump's campaign that the conservative ideal that right-wing youth are chasing after has degenerated into alt right garbage.
Considering that Classic Conservative has "Don't blame me, I voted for Ted Cruz" in his sig, I don't think he considers Trump the ideal or pinnacle of conservatism.