www.psypost.org/2020/05/meat-eaters-tend-to-have-better-psychological-health-than-vegetarians-56698
An interesting meta-study here assessing a number of other studies to conclude there is “clear evidence” that those who abstained from consuming meat tended to have higher rates or risk of depression, anxiety, and self-harm compared to those who did not.
No indication whether it's lack of meat making people unwell, mental health problems causing a susceptibility to vegetarianism, or some common cause for both.