TBH I found the FF13 review Jim made here more useful than most polygon reviews.
That said, I honestly think the "100% objective review" is pretty much the definition of a straw man argument. No sane person beyond some a few trolls or crazies here and there will make a comment about wanting a 100% objective review. They'll make comments about objectivity yes, however usually it doesn't mean what Jim apparently thinks it means. And quite frankly if this video didn't have a long review in it the main point of it could have been contained in a single tweet. And TBH points that you can do that with are usually very low on nuance and actual thought behind them.
The issue is that games reviewers have an audience. They have an audience because that audience wants to read/watch/listen to their reviews. The audience wants to do that because they feel that the review is giving them information and opinions on portions of the game that they're interested in. And when a reviewer changes his/her reviewing style and spends big parts of the review talking about things that his/her audience isn't interested in you get some backlash because you're not serving those customers of yours anymore. In a perfect world you'd just get less traffic because of this but this isn't a perfect world so people are going to let you know that you gave them your opinion on things that they were not interested in.
I don't want some "100% objective" straw review. I want reviewers on big consumer oriented gaming sites to understand that they're there because of those consumers and those consumers (or the huge majority of them) are looking for consumer oriented information and critique on some specific game.
I want reviewers to understand that there's a middle ground between listing facts and letting your moral and political world views color everything.
That middle ground is when you realize who your audience is, do your best to inform them as consumers, are capable of separating your own political views from your review when needed/wanted and also capable of including them when needed/wanted, you're capable of understanding that different sites, audiences and mediums will demand a different type of review with different types of information etc. For example on a PC oriented, no politics allowed forum you probably shouldn't write a review about the PS4 version and go in-depth about how that game offends you as a republican. Similarly on an agenda driven site that has an audience that cares more about story, characters etc. than tech specs you should probably not write a PC performance review with tons of benchmarks, graphical settings analysis and next to no character/story analysis. Both of those are bad reviews because they don't fit their audience.
Context and medium in which you publish the review matters. And you as a reviewer are not shielded from criticism or backlash when you fail to take into account the people (your audience, the users of that site, readers of the magazine, etc.) that give your review its importance.
I moderate a no-politics and no-religion PC hardware forum with gaming stuff on it as well. It's not impossible to keep politics and religion away from reviews and discussions if the specific audience or site wants that. In fact it works really well 95% of the time. There's a time and place for everything including religion and politics. And that time and place is not everywhere. I think it's pretty clear that a lot of people want to read reviews that let everyone from different countries, political orientations, religions etc. feel like the reviewer was there to help them make a decision as a consumer and didn't try to push his or her world view on the reader. There is HUGE value in consumer oriented informative reviews that hold back on the agenda.
And this is also why a lot of gamers are now looking to twitch and youtube for their gaming coverage. On those mediums they can see the game while a personality or reviewer plays it (this is specifically talking about let's play content or first looks, or some other very lightly edited content). Gamers can themselves see if the gameplay and content looks like it matches what the reviewer is saying. People on youtube and twitch feel more genuine as a result of this. There's much less opportunities to push an agenda or show the gamer something he/she isn't interested in. I even feel that Jim's youtube videos are much more useful and feel much more genuine than his reviews and jimquisition videos.
Jumping back to the "objective review" and the backlash against political / agenda driven content. Another issue here is review scores. All would be well if we lived in a perfect would where review scores existed in a vacuum and didn't directly affect the livelihood of devs. If scores didn't exist, metacritic wouldn't exist and no dev would have their bonuses or future of their studio depending on what score they get on metacritic. And at this point it would be perfectly fine to have reviews that go on an on about politics, moral issues, religious issues, etc. because those would just be sections of reviews. But the situation we have right now is that those issues affect the score, and the score affects the overall score on metacritic. Which means that we're in a situation where a game offending say polygon and kotaku reviewers because it dared to include boobs can mean the meta score gets dropped by some points (maybe 5-10%), the developers don't get their bonus, a sequel isn't made and layoffs will have to happen. All that while it's entirely likely that 99% of the people that were considering buying the game did not in any way care about the issues that polygon and kotaku did.
And if that isn't sad, wrong and something we should work towards stopping then I don't know what is.
So in the end the problems to this debate are mostly:
1) Don't strawman the "objective review" argument
2) Get rid of metacritic
3) Get rid of scores in general
4) Know your audience and medium
5) Understand that there are wrong and correct places for different types of criticism
It's not rocket science. It just requires some nuance an less of the "us vs. them" mentality that even people like Jim seem to subscribe towards, even without directly saying it. The world isn't black and white. There are alternatives to fact lists and raving morality policing. Please explore those alternatives and listen to your audience.