comment: I'd argue there's a perfectly consistent difference.
  In the examples you bring up, Warnock and Biden are saying that their religious views are binding on them: Warnock is a Christian, so Warnock should act with compassion.
  Separation of church and state is brought up when someone attempts to force their religious ethics on others, outside of the agreed-upon functions of the government (e.g. the common welfare and all that stuff).
  Nobody would care if an Evangelical Christian politician, who was gay, said "I'm just going to avoid romance entirely because I believe my faith prohibits homosexuality", which is analogous to Warnock trying to be compassionate because of his faith.