Kasich does not believe in gay marriage. He believes that it is not a big issue and one worth fighting over. More importantly, he points out that the courts have ruled on this so no sense spending time on it.
Kasich does NOT believe in illegals. He thinks that we need to redo immigration and then pass bills to deal with the illegals here. In particular, he is not opposed to seeing non-voilent ones be permitted to stay (I think he goes too far, but he has right idea; COMPROMISE). 
Kasich DOES support Common Core and he notes that it was developed mostly by BIPARTISAN GOVERNORS.
Kasich does not believes in expanding Medicaid, BUT he does not believe in simply dropping ACA. 
Kasich believes in science/logic and therefore, yes AGW. More importantly, Most intelligent conservatives also support science and therefore believe that this should be addressed. LP supports addressing this, BUT WANT ALL to address it, not America. 
The Kock bros ARE BAD. So is Soros. 
YOU are not a staunch cnsrvtve