It is, of course, bullshit.
Yes, Pew finds higher rates of self-identified Dems/Libs report having been diagnosed with a mental health condition by a medical professional at some point compared to conservatives or moderates.
Nevertheless, rates of struggles with depression and other mental health issues are the same across the political spectrum. The difference is SEEKING HELP.
https://publichealth.jhu.edu/2024/new-study-shows-bipartisan-struggles-with-depression-reveals-gaps-in-mental-health-care-access
A new study published in September in the Journal of Public Health Management and Practice sheds light on the mental health crisis gripping millions of Americans, and the findings suggest that depression is a bipartisan issue that affects people across party lines. According to the study, there is, however, a striking divide on whether people seek mental health treatment, with Republicans less likely to have accessed care despite reporting similar rates of depression compared to Democrats and Independents.
...this study finds that depressive symptoms are virtually indistinguishable across party lines. The data showed 25.2% of Democrats screened positive for depression, compared with 23% of Independents and 20.5% of Republicans. These differences were not statistically significant, meaning that depression does not appear to discriminate by political belief.
While depression itself is non-partisan, access to mental health treatment may be another story altogether. Among those who screened positive for depression, the researchers found that Republicans were significantly less likely than both their Democratic and Independent counterparts to have sought help from a mental health care provider in the past 12 months. The study also showed that, among those with depressive symptoms, 73.9% of Republicans had unmet mental health care needs, versus 58.9% for Democrats and 58% Independents.
On edit:
Which do you think is more likely to lash out or even become violent? A person diagnosed and getting the support and treatment they need, or a person who is objectively mentally ill who is NOT getting the support and treatment they need?
Give the rates of political violence on coming from the right vs progressives/liberals, I think the answer is pretty f-ing clear.