He’s a liberal, nanny state elitist, that has little conservativeism in him. Matter of fact, I have never, ever heard him mention Locke, Burke, Montesquieu, Hyack or any classic philosopher.( I don't think he is well read, nor formally educated about political economy, at all ) In short, if he were to be a conservative, he wouldn't know why.
I suspect most people take his constant traditionalism as conservativeness. They are in a common error.