If you’re in the US, or any country with comparable speech/press protection: the same rights that give them protection to publish. I know it’s unpopular here but social consequences punishing bad press behavior are effective, just like punishing bad politician or famous people behavior. This is sometimes paraphrased as “vote with your feet” or “vote with your wallet”, but lately it’s been maligned as “cancel culture”. Either way, you’re allowed to just call bullshit on a publication. You’re especially allowed to not consume it.
"Cancel culture" isn't choosing not to consume media. "Cancel culture" is actively trying to destroy it, like advocating lawsuits against Fox News, or deplatforming media hosts.
What you describe is how it's always been. Current "cancel culture" is nefarious as it actively tries to remove other's ability to access it. "Cancel culture" is authoritarian and undemocratic.
