Is your email urgent? If so, you should probably call [Name] at [phone number], and they will assist you. They aren’t in the sunshine – they’re still at 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.

Yes! I remember reading here the phrase: the default mode of clever is asshole. Meaning when trying to be clever backfires, you end up just looking like an asshole. I’ve given up the need to get laughs at my clever sense of humor while at work. I really hope that out of office message is for internal emails only, because the risk of this landing badly is too high.
I had a colleague who simply never answered her phone or set up her voicemail. She still listed the number on her business card and email .sig, she just never answered or checked voicemail. When she took a new job another colleague inherited her phone number and when he went to set up his voicemail there were basically eight years’ worth of messages left for her that he had to delete.