I have gotten weird pushback on this that people are offended that I would say I am out for religious observance, as if it somehow implies that my reason for being out of the office is more important (or inviolable) than theirs. I don’t even know what to do with that.
I find it rude, as well. If someone is emailing you (the royal you), it’s because they need something. Saying you’re just going to delete it without also giving that person a Plan B contact is totally rude. It sucks having to go through emails, it does. But it’s part of the job. In my role, I get requests from internal colleagues and from external partners. Even though I provide those partners with an alternate email to send their requests, it’s still my responsibility to make sure that the requests that were sent to me in my absence were handled. Saying “everything I’m sent will be deleted” just Would Not Fly in my industry.

If the visitors land your website after business hours or during holidays and do not get any response they might slip away. They could be important sales leads and losing them can impact your business.
An out of office message is a compact text that conveys the most important facts: How long you’ll be unreachable, when your contacts can expect an answer, (optionally) the reason for the absence, and, if necessary, a personal note. A referral to another email address, e.g. to one of your colleagues, is often helpful or even necessary.