I do not identify with any of the above categories. Some of my views are quite liberal, others quite conservative. A little libertarian, a little socialist, a little some other stuff I won't get into here. But I am ferociously anti fascist, in part due to the fact that I am a member of a group that fascists love to abuse.Here is an article for you to read. With a little bit of back reading and research you will find that many of the people on this site are Libertarians or classic Liberals, not conservatives, although there are those as well. There are middle of the road moderates, slightly left of center thinkers, and rabid progressives as well. Most intellectuals you refer to are academics, there are many intellectuals that are not in academia. https://mises.org/library/why-intellectuals-still-support-socialism
Not all academics are intellectuals. Many hide in academia in hopes of being deemed "intellectual", but have little in the way of academic inclination. A masters degree is a lot easier to get than a bachelors in many cases.
Intellectuals, as I view them, explore, and question the cognitive dissonance with permeates the various cultures around the world. Intellectuals introduce other ways of thinking, question the old as well as the new, and try to find better ways of thinking and doing things.
As for socialism... so few of us actually know what it means. The USSR was not socialist; it was authoritarian. China is not communist. Socialism and communism are names used to hide the true nature of what end up being authoritarian forms of government. Right wing individuals often attach the word "freedom" to things that actually impede the freedom of others. It is the same thing, with different labels, differing politics, but the same control freaks at the center.