And I would just like to say: yes, if you are offended, your feelings are valid. Whether people respect them or not is a different story. You're not entitled to respect for your feelings, but on the other hand, you're also not entitled to be a dick about people's feelings and claim you're just being rational and logical.
When you mock people for being offended and emotional, you are also being emotional: you're feeling very, very smug.
I also find it rather... interesting... that this comic reframes Dr Pulaski as the offended party, rather than Data, as it was in the original. I do sure wonder if there's anything about Dr Pulaski that a certain segment of the population would identify as emotional and irrational.