The phrase "moral crusade" refers to a dedicated effort by someone or a group to promote or enforce their own moral beliefs or principles on others. Full definition
At the Westminster conference, Robert George used the concept of neo-Gnosticism that he develops in this issue («Gnostic Liberalism») to analyze progressive moral crusades from transgenderism to doctor - assisted suicide. (firstthings.com)
Trying to mobilize such opinion by simply endorsing candidates, «scoring» their voting records, and lobbying for or against particular positions is secular electioneering, not moral crusading. (religion-online.org)