Let’s talk about Conservatives and Liberals, and let’s talk about those words and what they mean. Take a step back from politics and look at the roots of the words we’re dealing with, then dive back at what those words ought to mean to not sound contradictory. It is then that we can discuss the spectrum of attitudes that we hold and map it to any sort of coordinate grid.
The fact that right now conservatives and liberals are at opposing sides of the political spectrum is a little silly, and a great misnomer. The antithesis of a conservative is a progressive, and one of liberal is a statist. They address different things - one pair contests the shape of society, while the other contests the government involvement.
The word conservative comes from conserve. Conservatism’s main credo is that major changes in society should be enacted as slowly as possible, and those systems which have worked should continue to exist, since new methods are unproven, and society is expensive to experiment with. Their opposite, the progressive, wishes to apply the fruit on man’s thoughts, the latest hot shot theories and fads as quickly as possible, attempting a lot, and hoping some of it sticks for the better.
The word liberal comes from the same family as liberty and liberated. It refers to the government’s attitude towards its people. They are, in fact, liberated from the government - not bound to it by regulations and obligations. Statists prefer the involvement of the state to micromanage society for the better.
On this axis a Lenin would be a Progressive Statist, along with Hitler, FDR, and Obama. Of course their exact degrees would be different. A true libertarian would be a Progressive Liberal. Your democrat is a progressive statist, and your average conservative is a conservative liberal.
As a Republican I opt for a Conservative Liberal approach - I believe in government non-involvement, and that includes its non involvement in progressivism too, to a certain extent. And I believe in caution in the face of new ideas.
We can then apply this sort of thinking to specific issues.