The question is really how to optimize awareness & participation with personal wellbeing. There's a big difference between getting psychologically clobbered by the outrage engines of social media or TV news, and being able to take in and understand current events in a way that encourages contemplation of how to best participate.
One way is to focus our attention and efforts on the things we can control as OP mentions. Another is to shift sources from fast/reactive news to more infrequent and considered sources. Another still is to participate locally and learn things firsthand.
If I were to go around, attaching my real name or face to my opinions as some form of "participation" in society, I would be quite fucked. I don't call that a privilege by any means.
One may also act on those views believing they are helping society, while consensus in society views those actions as detrimental. A recent example of this is the rioters and insurrectionists at the Capitol believed they were doing something to help society, whereas society judged their actions otherwise.
A possible solution to this conundrum is to focus one's participation on areas that are broadly agreed upon to be beneficial to society, so as to avoid accidentally becoming part of the problem, or simply minimize blowback from a disapproving environment.
This is a solution that is intentionally sidestepping any particular ethical framework, which may guide one's actions toward different tradeoffs.
Another thing worth considering is not all participation in society need be political at all, nor attached to your real name, nor known to your employer. Those are conditions you've attached to your response that were not part of mine.
Perhaps there is a moral obligation for people with privilege to engage; but it's clearly not a practical necessity for change to happen. Given the lack of progress in Black civil rights ever since the 60's; as this discourse around "we all must participate!" has strengthened, it is far from clear that it is helpful.
I propose that the other way is best. Live your life, respond with genuine outrage when injustice crosses your path, and don't feel like media consumption fixes anything.
I fully agree media consumption doesn't fix a whole lot, and certainly not in today's media environment, I merely advocate for staying informed and engaged enough to discover a useful way to make impact. I want to live in a world where we mostly just live our lives as we please, but society's state right now is such that I don't think it will let us off that easy.
That in itself is an irresponsible view. Nobody has the power to change society. The power we have is to make arguments and present ideas and then sometimes society changes of its own accord. Nobody is powerless to make persuasive and compelling arguments.
I don't know what you mean when you say privilege. It is a very broad word. The powerful being privileged is something of a tautology, but the privileged are not necessarily powerful.
What I said before didn't imply people without power do not also have responsibilities, just that those with power have more, because of their position in society. Part (perhaps much) of that responsibility is to work towards a better society; I used 'fixing' as shorthand for this. In the US that is 'a more perfect union' but there are other concepts enshrined in other countries. I don't think this is a particularly controversial position to take.
Similarly the concept of 'with power comes responsibility' reappears throughout human history and I don't think is controversial.
Maybe we're in agreement on this, I can't tell from the way you're picking things apart. Anyway, I'm going to politely bow out.