Related: Google is doing this. https://www.allsides.com/blog/audit-finds-evidence-googles-b...
Anything critical of the current administration is not left-leaning either. In the past, most of these organizations have been critical of the Obama administration, but they weren't considered right-leaning then.
"Our Media Bias Ratings represent the average judgment of Americans. They are based on blind surveys of people across the political spectrum, multi-partisan analysis and other in-depth analyses as well as tens of thousands of user ratings. Our scientifically-generated ratings are fluid and subject to change over time as new information is gathered and biases change.
Unless otherwise noted as editorial content, all bias ratings are based on online versions of news coverage, not TV, print, or radio content."
Link: https://www.allsides.com/media-bias/media-bias-ratings
You can also see that they differentiate between fox's online news and opinion pieces, with the latter classified as being on the political Right.
Edit: I do think the separation of their opinion pieces from their regular news reporting is a little bit of a cop-out though.
Politically, Fox does not stay put. To maximize market share, they always want to be just barely to the right of their main competition. Since that competition has gone quite a bit left in recent years, Fox has followed. By some measurements Fox is now even slightly to the left of the average American. Fox will immediately move back to the right if the competition moves right, because Fox can't risk crossing over.
It's hard to imagine a mindset where you see media treatment of Obama as comparable to that of Trump. It's night and day in every possible respect. And the donation and poll numbers from these organizations, which are generally 90-95% Democratic-leaning, confirm that.
It's supposed to mean, would you treat blue-team or the red-team better for the same behavior?
> drone strikes
This was heavily covered. This was probably the number one thing that Obama was criticized for. I think most people agree that this is bad (for various reasons), though technically it is protecting American soldiers lives. Oddly, we don't hear much about the fact that Trump administration has relaxed rules and is performing more drone strikes [1][2].
> tear gas at the border
I also remember his immigration policies being heavily criticized. Yet, if you look at the policies of the current administration, they are objectively far worse. If the policies are far worse, it is consistent with a neutral position to be more critical of the current administration's policies than the previous administration's.
> gunwalker scandals
While they tried to pin Gunwalker on Obama, Gunwalker was really a Bush administration scandal that wasn't discovered until Obama [3][4]. That was an attempted political hit during an election year, equivalent to Benghazi. Despite that, it was covered even by the crazy "leftist" CNN [5][6].
If Obama had been meeting secretly with the Kenyan government to gather dirt on his political opponents, defending them every chance he got when it was discovered that they spent significant effort to influence our elections, and trying to remove sanctions against them, there is absolutely no doubt in my mind that this would be heavily criticized and covered by both CNN and MSNBC. I do believe MSNBC leans left.
[1] https://www.nbcnews.com/news/us-news/trump-admin-ups-drone-s...
[2] https://www.washingtontimes.com/news/2018/jun/7/donald-trump...
[3] https://www.foxnews.com/us/ap-exclusive-second-bush-era-gun-...
[4] https://www.npr.org/sections/thetwo-way/2012/01/05/144761413...
[5] https://www.cnn.com/2012/06/28/politics/holder-contempt/inde...
[6] https://www.cnn.com/2013/08/27/world/americas/operation-fast...
Google also rarely[1] promotes Chinese and North Korean state-sponsored media sources as 'top news', or Marxist-Leninist publications, or the moral and political degenerates behind New Trotskyism[2], but for some reason, that analysis doesn't take issue with this lack of 'balanced reporting'. It's only upset that a very particular, very narrow political spectrum of ideas isn't getting 50/50 coverage.
[1] Never?
[2] Isn't it obvious that we'd be better off without listening to them? /s
You don't even have to turn to foreign news for that. There's no shortage of diverse domestic ideas, that for some unfathomable reason aren't being promoted.