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.
Not me, but a friend of mine once received an OOO that simply said “I am having an out-of-office experience.”

I think this is great. A little too long, but it would work well as an internal reply in a large office with the right kinda culture. I’m imagining how useful it would be in my previous office with 300+ people that always had some “fire” or another to put out. I also appreciate how it protects the sender’s time off–at no point does it say “ok, fine. contact me.”
Thank you for your email. Your message is important to me and I will respond as soon as possible. Thank you!