Disrespectful rough dismissing Conservative (4)

I believe the answer is:

rude

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'disrespectful' is the definition.
(I've seen this in another clue)

I don't understand the remainder of the clue.

(Other definitions for rude that I've seen before include "discourtesy" , "Base" , "Uncultivated" , "'Bad-mannered, discourteous (4)'" , "Impudent" .)

I've seen this clue in The Times.

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