i seem to offend people often. sometimes it's because of their closed mind, other times it's my own fault.
when it's my own fault, i apologize immediately, if it's at all possible to realize i said something offending to them. it usually shows on their face, or they respond angrily.
apologizing and talking it out is a great way to get good friends and allies. it works much better than tiptoeing, i can get closer to people by being open and honest and take the consequences in stride.
not saying you should knowingly offend. just to be conscious of how easily you can trigger people without meaning to, and use surprise triggers as a way to get to know people better and let them know you better, rather than always fear hurting someone unintentionally.
trying and failing is the way we learn. it works as long as we remember to learn from mistakes, and not repeat them a hundred times before considering a different approach.