There are certain academic jobs such as Baylor or BYU that require a certain way of life. BYU, for instance, requires one to adhere to the Church Educational System Honor Code and Baylor typically requires a letter of recommendation from your Minister/Rabbi (their words) with one's application. For example, being in a gay relationship would be enough to be expelled from BYU.
These require a certain type of personal life choices and lifestyle, and, while they are very religious schools, there are other possible dealbreakers at secular universities. For example, secular schools have retracted offers due to the fact that the applicant for a faculty job is on the sex offenders registry.
There's a huge amount of gray area between these two data points that I have. Where is the line drawn on how much one's personal life matters at a secular school? What would have to be publicized about a faculty member's or applicant's personal life in order for the person to have an offer rescinded or tenure revoked? Is it only about the research/teaching/service, or is there any examination on the person's life if that common knowledge in the community?
My question is mainly about the United States.