HowardP said:Maybe "Don't be ashamed to come out with it." or even "Spit it out!" (meaning 'Say what you really mean!')
How about the expression, "To bury one's head in the sand" (nascondersi la testa sotto la sabbia, i.e. like an ostrich)? This is a pretty common idiom in English, and seems to have a similar meaning.
I think the translation would depend on the context. "Don't try to hide the obvious truth" may be a possibility.
I don't think that's the same as "burying your head in the sand" which means refusing to think about unpleasant facts even though they may have some influence on the situation you are in.