According to Gallup, "Fifty-eight percent of Republicans report having excellent mental health, compared to 43% of independents and 38% of Democrats. This relationship between party identification and reports of excellent mental health persists even within categories of income, age, gender, church attendance, and education."
The following chart shows that even low-income Republicans report better mental health than Democrats with similar incomes. As expected, Democrats with higher incomes report 17% better mental health than Democrats with lower incomes, but high-income Republicans report 19% better mental health than high-income Democrats and 36% bettter mental health than low-income Democrats!
Of course, Democrats and Republicans do not exactly map to L-mind and C-mind, but that is at least an approximation.
Some portion of the population will not participate in polls and others will tell the pollsters what they think they want to hear or what will make the pollster think more highly of them - or they may lie outright. Thus, despite the best efforts of the pollsters, the results may or may not represent the actual opinions of the total population.
Never-the-less, poll results may be the best information available for certain things. Also, the high visibility of polls indicates that media audiences tend to pay attention to them.
On the other hand, since the differences are so strong (20% difference between Republicans and Democrats) there is a good chance the conclusions are true. Therefore all you L-minds, if you adopt some C-mind attitudes, your mental health may actually improve (or, at least, you may think it has improved! :^)