That does introduce a significant conflict of interest in regard to research, though.

I disagree because their research is largely about improving sustainability, not about proving to vegans (who will never win anyway if we're honest) that meat is okay.

The meat industry is not going to advocate for its own demise

For that to be meaningful to a discussion about UC Davis' research, there needs to be a meaningful possibility that humanity is doomed without everyone going vegan. No matter how we coerce numbers, that's simply not the reality. If and when there is reputable research showing that meat is unsalvageable, then we can start the hard discussions. Until then, the idea that the industry that most benefits from research would be unable to ethically fund said research is just silly. Please check out the chain that led to an essay from one of the senior researchers of UC Davis' CLEAR center for more context.

if that portion of the institution is dependent on the industry liking what the research is saying

None of UC Davis is dependent upon the meat industry. They receive some funding for some of their research from it. Because sustainability means lower cost and the meat industry likes lower cost. It's the same reason solar has started to win in the business sector. Better environment is good business. Yes, if there's a secret gotcha where the 1 millionth cow will suddenly explode with anthrax, there might be an argument. But despite some mild disagreements with "how much GHG is bad", there's not really much to criticize them for. And as a reminder, ALL food sources hit the environment in various ways, and many plants do the same worse than many animals. There's no smoking gun, so I would be incredibly hesitant to disqualify reputable science over it.

Any study that is funded by the same people befitting from a positive outcome doesn’t mean its bunk, but it should automatically, at the very least, be viewed with a highly critical and skeptical eye.

What about studies paid for largely by sustainability groups, but backed by businesses because the outcome isn't "positive" as much as "here's how you can reduce the methane impact of your livestock allowing you to efficiently scale your operations and produce more food for less money"? You can understand why the latter, far more common in research, is worth it to everyone.