Marion, I seldom sing religious songs at Jewish homes (except for the few listed above, which are not strongly "theologically loaded").  Popular Passover or Hanukkah or Purim songs are OK, and songs about freedom, peace and brotherhood, but not being Jewish, I feel it would show a lot of chutzpah for me to sing the "more sacred" songs.

Most of my songbooks don't have sectarian songs in them (though a few songs--like America The Beautiful--refer to "God").  Unless the residents request a hymn (e.g., Amazing Grace), the only "religious" songs from the Christian tradition that I sing in Jewish homes tend to be the old spirituals like "Swing Low, Sweet Chariot," and "Michael, Row The Boat Ashore."  Many of these songs are based on scriptures shared by Judaism and Christianity (e.g., "Joshua Fit The Battle Of Jericho") and many have the quest for freedom from bondage/persecution as a theme (e.g.,  "Go Down, Moses,"  "Wade In The Water," etc.).  I use these around Passover especially -- as well as the Carter Family's "Little Moses."

I really suggest asking the facility's activity director for guidelines.  Some facilities have mainly Eshkanazi (sp?) Jews from Russia and northern Europe, some have a lot of Sephardic Jews from Spain, Yugoslavia, etc., some have about half and half, etc.  (One place in Seattle has warned me not to sing Yiddish songs unless I do an equal number of Ladino songs, to keep peace among the residents, who are split about 50/50.)  Some facilities are much more open to hearing music from non-Jewish traditions, including Christmas songs.  (One place in California the residents requested "Silent Night" and "Santa Claus Is Coming To Town.  At another facility in Seattle you'll get a lot of flack if you sing "Jingle Bell-- which has nothing to do with Christmas at all.)  A lot depends on the residents.  A lot also depends on whether the staff takes the attitude of avoiding any and all complaints.  (If you have one resident out of 300 who gets upset at "Jingle Bells," do you ban the song?)

Kinda funny story in this regard:
I was doing a concert at Seacrest Village in Encinitas, CA (a Jewish retirement community), and the theme was a Labor Day program, so I had included "Sixteen Tons" in my playlist.  It wasn't until I got into the song that I noticed the "Christian" reference --"...St. Peter, don't ya call me, 'cause I can't go... ."  Suddenly feeling terribly embarrassed and trapped, I blurted out "...Moses, don't you call me ... ," and finished the song with that substitution.  (I actually think I sang it "...St. Peter..." the first time and then made the ridiculous substitution -- like nobody was going to notice.  I even had the audience singing along on the chorus.
Nobody seemed offended--but I doubt that they would have been even if I'd sung the song straight -- which is what I should've done, anyway.  It's an American folk song about miners--not a religious song!