This is possible. But I think it's less about this and more about status marking. Joining the pile on is often a quick, cheap way to demonstrate that you care about the right things.
From my self-confessed but unavoidable smug vantage point of white privilege I wonder if being offended is something that needs to be disregarded. I'm trying to remember how it felt to be 'offended' myself and whether anyone other than me should have cared. Is it actually a form of power when one can choose to be offended and know that you can affect the actions of others by doing so?
Genuinely hurting people (emotionally) on the other hand is something different and I'd need to think a lot more deeply about that.