You may read articles like this one that try to explain why liberal/progressive women are less happy, less well-adjusted than conservative women. This particular treatment fingers marriage and religion as factors explaining the difference.
Such articles observe a correlation between A and B and propose causation of A by B. But correlation doesn’t demonstrate causality, it only suggests a relation of some sort.
I am inclined to go at this question from another angle. Political orientation isn’t genetic, it is a choice a person makes. So I tend to think being unhappy makes you liberal rather than being liberal make you unhappy.
People are happy or unhappy depending on whether the society does or does not “work” for them. Do they fit a comfortable niche, or feel unrooted?
Those who feel unrooted or a bad fit with society seek change, and become liberals, seekers of change. Those for whom society “works,” and provides a good fit, will like the status quo and are thus conservative, seekers of stability.
Faith and family, for those who have them, argue for stability. Those without are somewhat less “rooted” in society and seek change as it gives at least the chance that a better fit will be achieved following change.