I had an issue with my 200-500. I don't think filters caused the problem, it was just that my new D850 wouldn't play nice with it. I nearly cried when every photo I took was blurred. Terrible. Then I read up on checking focus. I did that and discovered that with my D850 I needed to set the Fine Tune to +10. Then photos were sharp and I was happy. I moved on from the 200-500 to the 500 PF and never had an issue with it. Why was my 200-500 so bad with the D850? I'd used it with a D7200 and never had a problem. Sometimes, I think equipment can be quirky. I think that's why they give us adjustment options.That's a more interesting question for me than for most.
The first copy of the 200-500 I got was downright awful and I sent it back. The second was clearly better, but still made me think something was wrong... until I took the UV filter off. I always used to put UV filters on lenses and never noticed and issue, but with that lens I found that with the filter on it was really very poor. I've since tried several filters with the same results. This got me to take filters off of all my lenses. I've also read some people saying that telephoto lenses don't handle filters as well.
However, when I ordered my 70-180 from B&H it came with a filter included for free so I tried it just for the heck of it and have found that it has no noticeable effect on the image quality even at the long end. I've also more and more begun to wonder if something is off with my 200-500 as especially past a certain (closer than I'd expect) distance the IQ seems to drop considerably. I've started wondering whether the way the filter impacts that lens might be associated with some kind of problem with the lens itself, but I don't know enough about the physics of it to theorize, so I'm interested to try the same filters on a new 180-600 and see if they have the same kind of impact or if they don't. The answer may help me finally get an idea of whether there is something funky with my 200-500 or if the filters are just all poor.