Much obliged to you for your email but our office will remain closed due to upcoming holidays. Unfortunately, due to this, we will not be able to send you an answer until 12-01-20XX. In case of emergency, you can send your queries to Ms. Medley at [website], she will answer all your queries. All delays are hereby regretted.
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.

We had someone at my old job whose auto-reply stated that they were at a “White Privilege Conference”. Granted, the conference was about dismantling White Privilege, but to someone outside our work who didn’t know that, I imagine that got quite the reaction!
Or, worse, when someone has left the organization and the organization hasn’t bothered to put up an OOO, so I’m just emailing a blackhole until I call or someone finally checks that inbox. I never fail to set up my OoO reply, and yet most of my external contacts don’t get them. Let’s say I work for LlamaCombs, with an name(@)llamacombs.com address, and this is a company who has two clients AlpacaBrush and VicunaShampoo. I work primarily with the second, and their internal directory lists my contact info as name(@)vicunashampoo.com. It works because any e-mail sent to the second address is auto-forwarded to the first. Except it messes up OoO replies big time. Because the auto-reply is sent to my own alternate address, not to the original sender, and I have no way to change that.