It's the same concept as "equal justice under the law," applied broadly. If a politician and a black laborer are both discovered to be thieves, both should face the same law and consequence, without favor to the former because he is a politician or to the latter because he's black.

So no, the treatment should not be tailored to the person where equality is concerned. Equal opportunity, equal treatment, with the understanding that people will always be unequal by nature and by outcome.