Tolkein was a hard-line conservative. I don't know why this question is even up for debate.
Absolutely - he was a devout Catholic who came of age in Edwardian times. He was no hipster, "modernist" follower of socialism, but a man who was fascinated by ancient notions of honor and valor. At the end of his life, he was bewildered by the way the hippie movement glommed on to his work the way they did.
But keep in mind Gandalf and the hobbits were potheads. The traitorous Saruman even chastises Gandalf a bit over that.. ;)