they send emails expecting an immediate response because they know you will respond immediately. i respond to emails within 24hrs. people know this, and don't expect anything faster. if somebody does expect a faster response, that's too bad. you need to reassess your understanding of rude and manage people's expectations of you. if somebody expects me to interrupt what i'm doing to answer their email, that's rude of them.
if anybody requires an urgent response from me, they can try a synchronous method of communication. in the meantime, i've got things to do.