When it comes to data, the 2016 National Household Education Survey by the National Center for Education Statistics shows that 51% of parents selected "A desire to provide religious instruction" as an "important" reason for homeschooling their children, and 67% selected "A desire to provide moral instruction" as an "important" reason for homeschooling [0, in bar plot form; 1, original data].
[0] https://responsiblehomeschooling.org/research/summaries/reas... [1] https://nces.ed.gov/pubs2017/2017102.pdf