Do you mean you don’t answer calls and emails right away, or not at all? If you aren’t responding at all when someone tries to communicate with you, then that IS rude. If someone calls you, and you are indisposed at the moment to talk to them, that’s perfectly reasonable to take their message and contact them when you are available to talk. The advent of smartphones seems to have brought on a whole lot of communication rudeness and entitlement. There seems to be a lot of people who not only assume that you are obligated to own a device that keeps you always at their beck and call, but that there will never be a situation where it is inappropriate, hazardous, or bothersome to answer them. This expectation leads to the rudeness of people staring at their screen when there is a live human in front of them trying to communicate with them. There doesn’t seem to be a consensus of what sort of communication is appropriate in what medium. For example, you don’t breakup with someone or fire them over a text message, nor do you attempt to have a conversation that requires long responses. I’ve actually had a coworker ask me a question like, “Do you have any recommendations for regarding a certain program” and asked me to text her my answer, as if I’m going to sit and type out several paragraphs of information on my flipphone, including answers to all her questions, while I’m driving no less! Some conversations are more appropriate on the phone or in person.
For the OP, my recommendation is to look inward first. Are you being rude, dismissive, or avoiding conversations that might be unpleasant but need to happen? If not, then it sounds like you simply need to set up a communication plan with the individuals who are expecting you to communicate with them. Explain that you can’t always be at their beck and call because you have to work, sleep, shower, etc. Offer them your preferred means of emergency communication. For example, between me and my husband, if we have an emergency, we use our cell phones. If the person doesn’t pick up, we call back a second time, right away. That is our signal that we need to stop what we’re doing and answer the phone. We don’t abuse that method. Short questions that don’t require explainations are best resolved via text. For non-emergencies, maybe email is best, or offer a good time to call. (remember when everyone waited to call after 8 because minutes were free then? That was good.)