That is a very present question when looking at a lot of think tanks and whatnot.
Personally, I'd say it undermines my trust in a few ways. The broadest is undue weight: if some kinds of opinions are being paid for and others aren't, we're going to hear more of the paid-for opinions. But it also creates more direct incentives to a) say what might be rewarded, and b) once on the gravy train, say what one's sponsors like to keep getting rewarded. And worst, I think, is that money distorts cognition. As Sinclair wrote, "It is difficult to get a man to understand something when his salary depends upon his not understanding it."
So for me, any conflict of interest like that undermines the offered opinion. It's somewhere between hard and impossible to know how much influence is involved.
I had a disagreement with a famous (in my country) snowboarder on the internet about this topic. He goes on secondhand gear and beginners snowboarding forums and suggests boards by the brand that sponsors him. I told him he should at least put on a disclaimer on his comments explaining he is paid. His reply was that he chose the sponsor because he likes the product. I still think it's immoral.
This is what all spokespeople are trying to convince you is happening. We only ask people to mention that they're sponsored, not to declare their current opinions are lies.
Personally, I'd say it undermines my trust in a few ways. The broadest is undue weight: if some kinds of opinions are being paid for and others aren't, we're going to hear more of the paid-for opinions. But it also creates more direct incentives to a) say what might be rewarded, and b) once on the gravy train, say what one's sponsors like to keep getting rewarded. And worst, I think, is that money distorts cognition. As Sinclair wrote, "It is difficult to get a man to understand something when his salary depends upon his not understanding it."
So for me, any conflict of interest like that undermines the offered opinion. It's somewhere between hard and impossible to know how much influence is involved.