The first problem is that in order for the thesis to be true, you would have to see editorial policy actively discouraging the publication of conservative viewpoints. Instead, conservative views are regularly aired in so-called liberal media.
Second, the entire idea of an atmosphere of political correctness as "stifling" implies that the media themselves are to blame, when in fact the media are simply covering their bases in response to criticism. This criticism comes not from the management of the media itself, but from the audience. In other words, crying foul at "stifling political correctness" smacks of whining about receiving criticism because one's words offend. It confuses the negative right to free speech - i.e., that no entity can stop one's words from being heard - with the positive right of preventing others from judging your words. It's not a cry for "freedom to," but for "freedom from."
I suppose it's been easy for me to hew to this opinion for much of my life because by and large, I've never been on the receiving end of such feelings of persecution. Recently, however, the incident with the BDS and Brooklyn college (and yes, I know I'm 2 months late) made me nuance this view.
My particular eye-opening experience has been triggered by a series of editorials I read on the subject of the BDS movement, a movement in opposition to Israel's current political status. I never really cared too much about it, to be quite honest, and their actual opinions or staffing matter little to what I'm trying to explore here.
The most recent headlines concerned the incident where BDS speakers hosted at Brooklyn College caused the college to receive a massive torrent of vitriolic criticism from media groups, the ever-predictable Alan Dershowitz, the Anti-Defamation League, and more significantly, ten members of the New York City Council. This also prompted a torrent of abuse on anybody who supported BDS or even the policy it espouses.
Here is where I have to make an admission: I am, frankly, not a fan of where Israel is going and what it is doing. Israeli claims of victimhood have started to ring very hollow to me when over my entire life (for what it's worth, I can remember news dating back two decades) Israel has looked like it's held all of the power in its bargaining situation with the Palestinians, and imposed what looks very much like a colonial land grab in the West Bank. At the same time even during the latest Intifada there was no serious existential danger. So, while I wouldn't support their methods (and I'm ambivalent about their stated goal), the criticism BDS laid on Israel didn't seem so off the mark to me.
Finding these people whose views I nominally shared being so heavily criticized it occurred to me that I might just be experiencing a variant of the "stifling political correctness" feeling, except in the form of "stifling suppression of criticism."
After thinking about it, though, I think there is a subtle line that can be drawn between allowing others to fully express their views and where things become inappropriate.
First of all, it is one thing to criticize a viewpoint and another thing to actively work to prevent that person from expressing their views. This speaks to the precondition for the stifling political correctness meme that I mentioned earlier, in that there must be people actively working against the expression of dissenting opinion.
I say this because a distinctive feature of the response to the BDS movement was the action taken by politicians and other people in power - notably not including the media or most secular academic institutions - to actively suppress speech and claim the right veto speakers. The New York State assemblymen and women are the guilty party here: the proposal to defund Brooklyn College for inviting people they didn't agree with to speak was a clear infringement on academic freedom and would have encouraged severe chilling effects on speech unrelated to social pressure*.
The second point where I find the response to the BDS went over the line was in secondary media. My alma mater's school newspaper, for example, published some editorials linking in exacting detail the ways in which the BDS movement had similar goals and messages to early, explicitly anti-Semitic movements against the State of Israel - not realizing that their argument was tantamount to a well-researched guilt-by-association charge. Others were not so subtle, and openly called the BDS movement and any that supported them anti-Semites, and labeled moderates who supported Israel but recognized the grievances of the Palestinians the same way. Those who expressed those views and added that they were Jewish suddenly became taunted as "self-hating Jews." Maybe some of them were, but there was no evidence of it that I could see.
In short, it was a witch hunt. And that was not the fact of the criticism itself that caused it to cross a line, but that this bile is typical and is often echoed in mainstream media once any criticism of Israel apears. Repeated in this way, it goes beyond attempts to shame and into the realm of systematic defamation**. And that's not, well, kosher.
* Some might argue that the chilling effects from allowing unrestricted public judgment are just as real as actively trying to defame the speaker or impose restrictions from on high. While this is true, there is also a reason that social pressure should be allowed to have this effect. A better writer than I put it thus:
Political correctness makes us feel bullied, pushed around, afraid to speak our minds, careful with our words. That’s not always a bad thing. We should be sensitive to the way others see things. We should hesitate to give offense. Though we may feel muzzled by P.C., sometimes our silence really is golden. The struggle for social equality is clinched in the awkward pauses of unuttered jokes.** There are certainly parallels to the repeated accusations of racism that are often trotted out against conservative politicians. I am uncomfortable with these assertions as well as they cross the line in the same way that accusations of anti-Semitism do. To be fair, many of these assertions claim to be backed by "evidence," but barring something outrageously obvious most instances I've seen point to racism as one of many possible proximate causes, and not the most likely one either.
Cultures evolve by constantly redrawing the bounds of the socially acceptable, and we inevitably disagree over where those lines should be drawn. It’s natural to resent one day finding oneself on the wrong side of the line, and to push back against the feeling of being pinned in by social pressure.