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 actually stopped changing my VM and out of office right before I left, bc I just did’nt care anymore lol. This was only one of a number of things that this company did that was bonkers.

I’ll be back on [DAY OF WEEK], [DATE]. No explanations, no apologies, no promises to respond, no redirects to other colleagues. It works.
To remind us – as if we needed reminding, as we vainly strive for ‘inbox zero’ – of just what a time drain email has become, Kay Woodward, UK-based author of What Would She Do?, has wryly channelled one of her book’s real-life heroines, Emmeline Pankhurst (and Pankhurst’s movement’s motto) in her OOO. “Deeds, not emails. That’s what the Suffragettes need. And let’s face it, I’m probably in prison anyway, so couldn’t reply even if I wanted to.”