You can choose whether to nurse your offense or not nurse it, and you can choose whether to suggest to others that they should be offended. Reactions that are involuntary in the moment itself are sometimes voluntary in the longer run.

Taking offense is a tactic in politics and social interaction however as in 'the politics of offense'. People will tend to use the tactic more when it appears to be successful.

Get a group of friends where you constantly make (facetious) offensive remarks at one another's expense, both about individual qualities and group identifications. Eventually, having been called a filthy whatever-ethnicity or a loathsome whatever-sexual-orientation (including loathsome heterosexual, hey why not?) or a Christ-killer or a baby-eating atheist so many times, the emotional impact of such statements will be dulled, which will improve your ability to understand your actual objections and react usefully when you hear people seriously say such things. Worked for me!

I think it's possible to work towards not being offended by such things as remembering the times when one was accidentally offensive, by checking on whether one's standards are reasonable, and by evaluating actual risks of what the offensive thing might indicate.

That doesn't mean one can or should run one's offendedness down to zero, but (depending one where you're starting), it's possible to town it down.