Out of curiosity, are there any institutions that meets a “pure” research standard? NIST?

Or is that standard unattainable because undue influence exists everywhere?

Influence exists everywhere because without influence the studies wouldn't exist in the first place.

And people need careers, successful publications and grants make that possible.

That isn’t to say everything is trash— lots of good stuff is still done with these requirements.

Unless you have a wealthy aristocracy and some of them are bored so they create a lot of the major science of past couple of centuries.

Get a private wealthy benefactor that likes your work, then you can avoid undue influence.

Now the influence just comes from the wealthy benefactor and his interests

Works best when the benefactor is your dead parents.

..until the wealthy benefactor decides to exert it anyway

That's in principle what academic tenure is for, it guarantees independence and research freedom. And while you may talk about how there's always this or that political topic that anyone will shy away from, at least in the hard sciences I think academic freedom is largely intact.

In a company you can always be fired and the singular goal is the bottom line. Much more so since modern companies seem to not operate with the mentality of the old corporate research labs like Bell, but keep a much tighter lid on things, always pushing for products.

While true, are these biases impactful in the same ways?

Bias will always exist. The nature of that bias and the degree of impact will vary.