Uh, no. Mental health is an entirely good thing. Why on earth would anyone stigmatize it?
Anyway, I agree that conservatives seem generally happier as a group than far-left liberals seem. Yes, we recognize that there is injustice in the world, that there are problems in the world, but we don't obsess over it; instead, we work to correct it. But we don't work to correct it by pigeonholing everyone into little groups based on their skin color, ethnicity, or sex. We don't pit groups against each other; that solves nothing and increases tension within and among the groups.
Instead of, for instance, telling black people, "The police are evil and hate you," we say, "Most police are decent officers who want to help you. Sometimes, there are rare, genuinely bad officers. Sometimes there are officers who didn't adequately learn their training. Some officers are just inexperienced, and someone winds up dead. That is horrible, and we hate when it happens, but it shouldn't always signal a call for a race war."
That's the difference between how I think most conservatives think and how most of the far-left progressive liberals seem to think. The conservatives stop and think, generally, and the progressives don't seem to. They're all caught up in their emotions, and what they feel isn't healthy.
Look at Joyce Reid's admonition to her fans to stay home and not visit relatives over Thanksgiving. I'm not about to let politics get between me, my family, and cornbread dressing. I can eat Thanksgiving dinner with Alexandria Ocasio-Cortez and just let her rant while I apply myself to the meal. Or I can deflect her ranting into more interesting topics in between bites of cranberry sauce. I would be astonished at anyone who did take Joyce Reid's advice seriously. She sounded, frankly, paranoid.
That said, there is plenty of mental illness among conservatives, too. I've heard some real wacko opinions from occasional people on the right. There may be people who consider my own opinions whacked.