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.
I do this because my industry’s norm is that people check their email on vacation, at least once or twice, but I don’t do it. I don’t have work email on my phone so it’s technically true.

Some of my coworkers have started putting “Thank you for your email” at the beginning of their out of office replies. Management loves it, but I think it’s too ingratiating and I cringe when I read it. These are junior-level staffers, so maybe it makes sense in that context? Anyway, I refuse to put that in my out of office messages.
5.) Gentile Cliente, il nostro ufficio sarà chiuso dal 24 Dicembre fino al 2 Gennaio. Potete contattarci come sempre da Lunedì 5 Gennaio. Auguriamo a voi e alla vostra famiglia un felice Natale e un Buon Anno Nuovo di successo.