I think important context here is that no matter what the details added were, it always had this aggressive tone of “I’m taking a break and breaks are IMPORTANT”. Which I agree with, but it felt like it was almost aggressive/accusatory, and more importantly: this person was without a doubt the meanest, cruelest, least understanding and empathetic person I’ve ever worked with who ran her staff into the ground with urgent demands and expectations.
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.

“Thank you for the message. I am currently out of the office and will not be back until [date]. I shall reply to your message as I return. Should you require any immediate assistance, feel free to contact [person] at [phone number] in my absence. Have a wonderful holiday season.”
If you’re out sick or caring for a loved one, you may not feel comfortable sharing the details. You can simply use words like “family situation” or “family matters,” which Smith says automatically garner some goodwill.