I can't tell you about baseball at all or what the fans of that sport think of their officials, tbh.
But honestly, NFL refs are about a million times more respected by fans than any football referee I've ever seen in my life... and quite frankly, that's because they make the correct decision most of the time. The times where calls are disputed, it usually gets talked about for weeks. You compare that with the refereeing oddities we see in England now and you get at least 1 high profile error each day there's a side playing it feels like. With the NFL referees go to review the video footage, they overwhelmingly make the right call.
The one time I'd heard of NFL referees being shite consistently was when the actual professional referees went on strike and they had to bring in school referees who were nowhere near as good (a lot of them are trying to become actual NFL refs and tbh it's a hard job to get, with lots of people trying to get that job and with the bar for entry being very high). It was basically like having League 1/2 referees in the premier league, it was incredible how bad they were. I think that might have actually been my first or second year in America, but it was definitely the first year I'd tried to get into the NFL so I remember that pretty vividly.
With the actual referees that are supposed to be officiating, I only really remember one really really egregious wrong call after it went to video review. NFL referees aren't perfect... but they're really fucking good in comparison to referees in a lot of sports. But it's American football, it's a sport where there's a shitload of dead time - the referees aren't getting absolutely knackered constantly running everywhere. They've also got huge teams of officials and (as far as I know because they want to be a bit secretive about VAR for some reason) use far more camera angles for reviewed decisions.
So there's obvious differences between the two sports - but I do think there's things we can learn from the standards the US expects of the NFL referees. We could go one step further and add a bit more transparency to VAR review by having the referees mic'd up so and asking them to explain their decision-making process to the TV. The NFL doesn't do this, but that short term XFL league from earlier this year had it (before COVID killed that league off) and... it was actually pretty great, and tbh any sport with video review should have the ref mic'd up.