Honestly this seems like the inverse of Dorito Pope.
With something like Dorito Pope, the concern is that we are not getting the journalist's true opinion. They don't really like Doritos and Mountain Dew, they are in fact getting paid to endorse them, and so their endorsement should not be taken at face value. It can't be trusted. Similarly, if a journalist has invested in PepsiCo stock and they then go on to write a column about how no, really, they love Doritos and Mountain Dew and you should try them for all your gaming needs... well, we would be right to be somewhat suspicious of this and to think maybe they have a conflict of interest. This looks and feels pretty dishonest.
With Patreon, the situation is inverted. The journalist writes a column about how much they love Game X and how they totally recommend it. But wait! They've also given money to the game developer via Patreon. Can we be sure they're being honest about loving this game? Yes, we can be very sure they love it since they've gone so far as donating their own personal money to the dev. There's no conflict of interest here; there's nothing to be gained for the journalist except that more people will hear about and try out a thing they like, which is standard for any kind of review anyway.
In short:
Journalist has some external stake in a matter -> journalist gives their opinion about that matter -> we can't feel confident that they were honest with us.
Journalist has no external stake in a matter -> journalist gives their opinion about that matter -> journalist further confirms that it really is their opinion by spending money -> we can feel confident that they were honest with us.
I really like the podcast Writing Excuses, about writing fiction, done by several professional SFF authors. Let's say that I go into a thread about podcasts and say "hey guys, I love this podcast Writing Excuses and I highly recommend it." Then someone else comes into the thread and says "guys you can't trust him, I know for a fact he has donated money to keep this podcast going." Do you feel more or less confident that I was honest about my opinion after hearing that?
I think it was clear earlier that I basically agree with you on this. But the standard defense of this type of "appearance of bias" rule runs the argument in a different direction from how you're thinking it has to go.
That the journalist donated to, say, a political party is not what
makes them untrustworthy. It
shows that they are untrustworthy. It's not about whether they're honestly partial to whatever-it-is; it's that they're partial to it full stop.
Game out how this usually works. Something newsworthy has happened. Someone writes about this newsworthy thing, with implicit or explicit judgments. Maybe Obama comes out with a budget proposal, and someone writes about how the budget proposal is socialist and is punishing success, etc. Lots of people are going to be very interested in knowing what that writer's opinions were
before Obama released that budget proposal. If the writer is a Democrat, the writer's judgments are going to be taken to be a lot more reliable than if the writer is a Republican, because of course a Republican would say that about an Obama budget. Donating to Republicans doesn't
make pundits more likely to unfairly criticize Obama, but a pundit who donates to Republicans is more likely to unfairly criticize Obama than a pundit who does not. Pundits who would otherwise like to donate to Republicans therefore have a reason not to, because if they spend a lot of time being critical of Democrats they want to be perceived as being as left-wing as possible (usually "moderate" is all they can plausibly go for) because it signals to the audience that the pundit's judgments aren't knee-jerk partisan responses but are considered and unusual departures from the norm that ought to be listened to.
That's basically a good strategy for an audience, if everyone is accurately representing their bias. People are going to pay less attention to your recommendation of this dumb podcast than they would to my recommendation of it if I make clear that I don't even
like writing and listened to an episode only after you made me but I ended up loving it (note: this is not true and I am not endorsing this dumb podcast). It's got to be pretty good if it turned someone very likely to be a non-fan into a fan. Obviously the problem is that people have a lot of reason to misrepresent their prior biases (see all the faith-affirming stories that start out "I used to be an atheist..." or "I always thought homeopathy was nonsense..."). Edit: Or to make this more gaming related: "I own all the consoles..." (whether true or not).
So the media's ended up with a rule of avoiding any appearance of bias. This satisfies the people who don't have the game theory to grasp that in fact a lack of appearance of bias is not a trustworthy signal given that there are strong incentives to avoid an appearance of bias, but I don't think it's fair to say that this is all about fooling the rubes. People in the media
think of themselves as unbiased, or as delivering the news or making judgments about the news in some sort of ideally neutral way. And so that's what they want to communicate to their audience. Even if they personally are huge fans of Obama's policies, because (they think) they're providing a neutral viewpoint on them, they think it's important to signal that they have that neutral viewpoint, by not doing the sorts of things that would reveal them to be huge fans of Obama's policies (because this would lead to what they think is the mistaken impression that that's coloring their reporting and punditry).