I believe the relevant saying is "Offense is taken, not given".
Of course it's worth considering why the person is offended, because you should never be purposely upsetting someone, but at the end of the day it's their problem, not yours.
Because if you think about it, is it not equally oppressive for you to try and control my thoughts and opinions just because you're offended?
The constitution literally allows for a person to use his words to be a complete jerk and not feel bad about it. But at the same time, the person who's at the other end of that verbal diarrhea can use the same right to tell him what a jerk he is.
And that's the beauty of it.
Basically, offending people is you exercising your right to free speech, and them telling you they're offended is using that same right. But you reacting to their offense is your choice. You aren't legally obligated to change your message just because people are offended, you're at most socially obligated to do so.
But nevertheless, the choice is yours.
With these choices come responsibility. Yes, you have the right to say whatever you want (provided it's not directly resulting in the harm of others). However it is their right to be offended.
OK, so I have the right to offend people, you have the right be offended, and to tell me you're offended, and I have the right to roll your eyes and tell you to fuck off. So far so good? OK.
But you also have a right, in turn, to not want to associate with me anymore. I can't make you listen to my opinions.
If you decide to not share my company— in whatever form that may be: in person, on TV, at a rally, or on the internet, that is also your right. And if enough decline to participate in my rants, and you lose your platform, that's simply the way the chips fall.
A person can complain all they want about their free speech being stripped, but that's not what's happening. That is the world saying "Hey! You're a jerk and we're not going to listen to you," which again, let's not forget is our right.
Of course you can complain about it, and we are allowed to roll our eyes at you.
And thus the cycle of offended offenders keeps going and going.