Their conclusion is that simple social involvement is not predictive of mental health outcomes, you have to know type of social involvement. Attending church is associated with positive mental health outcomes whereas "participation in political/community organizations was associated with an increase in depressive symptoms." I would have to guess that a lot depends on the nature of your local political and community organizations.
Overall, they conclude:
Our findings suggest that social participation is associated with depressive symptoms, but the direction and strength of the association depend on the type of social activity. Participation in religious organizations may offer mental health benefits beyond those offered by other forms of social participation.Not quite what I would expect but interesting food for thought.