There is no right to offend nor a right to not be offended. Offense is only taken, never given. Offense is like beauty — in the eye of the beholder one mighty say.
You can try to offend people and fail, you can try to not offend people and fail. This happens because taking offense is a choice. Taking offense isn’t the same thing as not disagreeing, accepting, or tolerating something someone says, despite those too being choices.
Being offended is a mental state under our control. As such we do have a right to be offended and a right to choose to not be offended. But because you can’t actually make someone offended there is no right to it. Similarly because we choose to be offended or not, there exists no “right to not be offended” in the sense of preventing others from speaking or doing something we choose to be offended by.