I think in general it is rude. Unless for example that is the situation when my dad was retired (he went back to work) and sent us up to ten emails a day with some political message and then was upset we didn't reply. I told him I am busy all day and cannot possibly read and reply to all that as it is not even something I understand (some conspiracy theory). Or he would send offensive emails and expect replies. Not gonna happen.

Also there are some circumstances like when I am depressed and pains to even talk to anyone I send a text to my mom or borther that I would reply tomorrow but those are special cases. In general not replying is RUDE. I recently dated someone like that, it was awful, I ended it, he never replied but I yesterday discovered some evidence that he perhaps was seeing someone else the entire time. So not replying at all or waiting long is a major RED FLAG for me.