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.
Website: https://asthedrillturns.com/2019/02/18/dental-office-voicemail-etiquette/

I say this as someone who used to have a chronic problem keeping up with my personal voicemails. But I got voicemail transcription set up so I can read them now, because just ignoring important phone calls has consequences. I can’t imagine trying to just duck them in a professional job where I had a phone number, and therefore an expectation that people can call me!
Nowadays, it’s getting increasingly more frequent for criminals to use the information we share to their own advantage. They could even use that information to break into a home or an office.