I am having trouble determining whether this letter from the CEO of Target, responding to criticism of his personal decision to donate money to a Republican electoral candidate who is quite clearly hostile to equal civil rights for gay people, is really an apology. Although he does use the word "sorry":

The intent of our political contribution to MN Forward was to support economic growth and job creation. While I firmly believe that a business climate conducive to growth is critical to our future, I realize our decision affected many of you in a way I did not anticipate, and for that I am genuinely sorry.

The fact that he feels the need to add the word "genuinely" ahead of "sorry" suggests that he is worried that he will be regarded as insincere.
My take on this letter: I think it does not really qualify as an apology. He does not say "I should not have donated money to this candidate". He merely apologizes for upsetting people, while neatly side-stepping the root cause, namely that he donated money to a candidate who appears to be of the opinion that gay people do not deserve equal civil rights (what part of "we hold these truths to be self-evident; that all men are created equal" do these people not understand?).
So my verdict is; nice try, but I think I am about to add Target to my list of Places That I Will Not Buy From.