Nobody "accepts" fWAR or bWAR as true value, and I can understand that seeing some wide differences in a few selective players can make one feel like these guys are just stabbing at it in the dark, but they are actually using some pretty sophisticated and scientific methods based on what value certain acts done in baseball lead to runs or allowed runs.
To me, I'm thinking they do a better job at determining the whole value player A vs player B than I can do in my head, based on just my own limited observation and a few crude stats that often miss the mark, too.
I remember when RF/9 first came into popularity. It was certainly eye-opening to see one SS could make 100-150 more plays than another in the same amount of innings, but then people started saying, but player B plays on a team with a lot of strike out or fly out pitchers, so it's skewed. (They were right to a certain degree.)
Now, fielders are observed by trained and calibrated professionals. Does that make it perfect or fool-proofed? Hell, no, but at least someone is watching every play of every games- something I don't even reach 1/29th of over a season. They measure how many playable balls are hit to a player and how many times an out is recorded. They measure difficulty factors and error rates. It has to be better than what I or any one person can do in their head by just watching 162-maybe 300 games a year.
It's far from perfect but, to me, it beats the hell out of my own observations. I try to watch every single play of every single Sox game, every season. I rarely watch any other games, so I just see the opposing players vs our own players. One observation I have made is about fielding- something I loved and was good at when I played the game for a couple decades. I notice when the opponents make spectacular play after spectacular play at SS mush more than ours does. I'm thinking, to myself, man-o-man, I wish we had a SS who could have the range and athletic ability these other teams have. Then, I look at UZR/150 and DRS, and my observations are confirmed. It doesn't mean I think my opinion is 100% fact, but I do convince myself that I was right all along.
I try hard to not sound like I am stating something that is not up for debate, but that does not mean I don't hold some opinions I think can not be changed. I assume everyone feels the same way about some of their beliefs, and some of those beliefs might be polar opposites to mine, I'm fine with that and actually welcome that. I love a healthy debate based on logic, reason and evidence. I have changed my opinion on a few things. At first, I thought Ellsbury and Nomar were obvious plus defenders, but over time and deeper observations, I came to realize they were not. Actually, Nomar was okay early in his career and Ellsbury turned into a plus defenders after a few years, but I do realize I can and have been wrong many times over and will be again.