For non-urgent inquiries during my absence, you can contact [Name] at [email] or [phone number], and they will be happy to assist.
“I am spending time with family today – some things are MORE important than work.”

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.
Boss would put up an OOO when attending an event off-site, but would still be answering their emails, which meant that I would get “Boss said you were the correct contact, can you help?” Inevitably, I would respond and, two hours later, Boss would too, cc-ing me on the original email in which they shared the exact same info I had earlier that day. It was MADDENING.