Wilco, I play in Jewish retirement homes and convalescent centers a lot, and although some of the activity directors bend over backwards to avoid offending the few residents who are hypersensitive to anything remotely associated with Christianity (e.g., not singing "Let It Snow!" or "Frosty The Snowman" because they tend to be sung at Christmas time), I have had no problem with songs about God or Old Testament figures if they make no reference to Jesus, the resurrection, etc.

Joshua Fit De Battle Of Jericho, for instance, is strictly an account of the battle -- no reference to salvation, heaven, etc. When I do Go Down, Moses -- usually in connection with Passover --, I tell them about the song's history re Harriet Tubman (a woman called "Moses"), too. The struggle of American slaves seems to be something they can see as parallel to the Israelites' struggles in their own captivity and search for escape from bondage.   I use these along with Dayenu and other passover songs. If I ever have any feedback that someone is offended, I will be glad to change the playlist, but so far they seem to be accepted. (I'm not sure how many of the Jewish residents are very familiar with The Carter Family, anyway.) If I do Swing Low, Sweet Chariot (which I usually don't), I tie it to the underground railroad and its "code message."

I DON'T do Jacob's Ladder, BTW! (Think about the lyrics and you'll understand why!)

Genie