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.
Let’s be real, the majority of the thousands of emails you return to after being O.O.O. will be spam and salesy marketing drivel – any legitimately important emails will probably get lost! Unless you’re Barack Obama, just send it when they’re back.

A thing my employer does is when someone leaves, they just shutoff the email. So someone goes to the trouble of writing an out of office explaining that they have retired or accepted a job somewhere else and where someone can go for help and IT just nukes the email address 24 hours after the person leaves. Then whomever was contacting them has no idea where to turn next. It is a terrible policy.
I could see the benefit if someone needed to ask something before they left. It seems courteous?