While you shouldn’t use a vacation message like the first example in this article, it doesn’t mean you can’t have a little bit of fun with your emails.
If you’re traveling to a remote, mountainous area, why not jab some fun at your lack of WiFi in your autoresponder? Plus, that makes it less likely that people will expect an immediate response or continue to email you after the first try.

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.
The Uniform Holiday Bill (Public Law 90-363 (82 Stat. 250)) was signed on June 28, 1968, and was intended to ensure three-day weekends for Federal employees by celebrating four national holidays on Mondays: Washington's Birthday, Memorial Day, Veterans Day, and Columbus Day. It was thought that these extended weekends would encourage travel, recreational and cultural activities and stimulate greater industrial and commercial production. Many states did not agree with this decision and continued to celebrate the holidays on their original dates.