I can't recall a single time that President Obama even intimated that somebody was a racist because they criticized him.  Or are you just throwing out a completely baseless generalized assertion as a fact?
People can absolutely criticize the President and should when they disagree with policies or think his behavior is inappropriate to the office.  But over the last 8 years so much of the criticism was so baseless, personal and devoid of any facts or logic that a reasonable conclusion would be that it was solely based on something else, like the color of his skin.
Do you really think that the whole birther bs, in which the current President had a large hand in, would have ever happened to a white person?