The form of
affirming the consequent is:
If P then Q.
Q.
Therefore, P.
Your argument is:
1) If homosexual & heterosexual slurs were the same (P), then you should not get offended (Q).
2) You did not get offended (Q).
3) Therefore, homosexual & heterosexual slurs are the same (P).
It's a bingo! But is your formulation of his argument accurate? You said
The person claimed that because he, as a straight man would not get offended if someone tried to insult him for being straight, that must mean that the homosexual slurs are just as inconsequential.
1) "Straight insults" to a straight man are inconsequential (e.g., "You like boobies! ha ha!").
2) "Straight insults" are of the same significance as "homosexual slurs." (implied premise)
3) Therefore, homosexual slurs are also inconsequential.
This might be a more accurate formulation of what he is arguing*. As you can see, there is a major problem with premise #2 and therefore, the conclusion does not follow. This is not fallacious; just a bad (unsound) argument.
* The fact is, we should be asking the person if this is what they meant. The person could have very well mean exactly how you presented the formalized argument.