I wouldn’t be offended or consider saying anything to anyone who included this in their out of office message, but even as someone who is in a religion that forbids use of electronics on most holidays, I still think this message is 1) TMI; 2) doesn’t convey what it needs to convey unless you are explaining that you don’t use electronics during holidays, in which case you can just include that you won’t be checking email without including the religious explanation; 3) would come across to me as inclusion of personal information I don’t need, which would therefore strike an unprofessional tone,and I wouldn’t understand why you felt the need to include that info. How about “I’m out of the office without access to internet or email until (date). If you need assistance before this date, please contact…” Like I said, I think your colleagues are overreacting, but in general I would advise to leave all personal information out of your auto-reply — vacation, medical leave, religious observance, etc. — people do not need to know why you are out.
Exactly. It doesn’t matter if I’m sitting on the beach, on my couch, or in a hospital bed–I’m not reachable and you’re gonna have to wait until I get back or contact someone else.

5.) Dear customers, our office will be closed from December 24 through January 2. You can reach us as usual on Monday 5 January. We wish you and your family a merry christmas and a happy and successful new year..
This makes a lot of sense to me, since surely in the 3-4 months people tend take as leave in the US, your issue would have been resolved. Also for parental leave, most people delegate ongoing projects to some specific person, so anything that’s still going to be going on months from now when you return is getting handled by someone else.