I've learned that 'do' has to stand with ordinary verbs, for example 'I don't love him'. Therefore, I feel confused when hearing people say 'don't be shy'. I wonder why 'to be' and 'do' can stand together.
[You] be good is an "imperative" utterance (instructing someone), where You are good is a "statement" (describing someone). When negating the imperative we usually include an auxiliary verb (often, "do-support"), giving Don't [you] be naughty today (Be not naughty is antiquated phrasing).