For comparison my current (not great) boss sent an out of office recently detailing how he would be out because he was on his personal sail boat all day, sailing from vacation destination X back to our port city. At length. In a pandemic. When we all had our wages frozen at the start of the crisis.
Using autoresponder emails when you are not available at the office is a part of the professional communication between business associates. That said, you should be careful about the information you are sharing in your OOO messages.

I work in a role where someone else has to cover when I’m out, so most things do get taken care of. I have never been in a position where I could delete all emails without ruffling some serious feathers, so while I appreciate the motivation, it’s a completely foreign option to me.
I can see why you’d have a negative reaction to it–that’s how I felt the first several times I heard about these kinds of emails–but I don’t think it’s actually rude (unless they’re saying “if I get emails from Ali G, I’m deleting them”). The wording of the email can be rude, but the general concept of this kind of email isn’t.