There are countless millions of people with no careers at all. Clearly, our society doesn't believe in a right to having a career at all, let alone a right to keeping one's existing career.
If we're worried about the threat to PewDiePie's ability to make a living, to his life, liberty, and pursuit of happiness, it seems like the fundamental problem is not with people on the internet having opinions, it is with the system where losing a career threatens all those things. Fix capitalism, implement a UBI, whatever, and then his loss of a career wouldn't seem like a threat to his ability to live a fulfilling life or to reach an effective means of speaking to people.
The same argument can be used to say, "Your opinions have consequences. In this case, shutting down the TSA's security theater program put a lot of TSA agents out on the streets. You have to take responsibility for it." Or "In this case, Edward Snowden almost ruined the careers of many NSA spooks who could never make it in the private sector." Or many similar things. Would you agree those are bad arguments for not fixing the TSA or reforming the NSA?
Just like no one gets to decide what kind of jokes are allowed to be told, no one gets to decide how someone reacts to those jokes.
We do have a serious problem that someone can say things in what feels like private, to what feels like a private audience, and they can attract a global audience very quickly. I said lots of dumb stuff both in person and online (on AIM or Xanga or something) as a teenager, and those are gone from the internet and that is very good. That seems to no longer be true for today's teenagers. I'm worried about this, and I'm specifically worried about the inevitable media circus once the generation that grew up on Facebook and Twitter starts running for elected office. Democrats will be vilified for liking Ayn Rand for a few weeks in 10th grade; Republicans will be vilified for liking Karl Marx for a few weeks in 11th. If you remember the hullabaloo over that one Bernie Sanders college essay, imagine that, 24/7.
But I don't see the "destroyed their career" argument being applied to teenagers; I see it being applied to people who basically have communication as their job. PewDiePie's entire career involves making as many people as possible watch him talk about things. Of course people are going to have opinions on what he says, and of course his career is going to be affected by whether the general public likes what he has to say. That's the career he chose.
Yeah, and people saying "Death to Jews" managed to murder six million of them. Yet apparently you think that is funny and beyond reproach, while taking issue with it is a serious problem.
You're welcome to your opinion. But you also have to take responsibility for it.