The majority of F-Class shooters I know strive for the best possible accuracy they can attain during load development, at least the ones that are regularly winning matches. I've never heard any of these folks talk about giving up accuracy. They are likely not achieving BR precision, but that may have more to do with their setups, such as the bipod in F-TR, and/or requirements, such as maintaining good ES/SD over long strings of fire, which will help minimize vertical at longer range. To some extent, the differences between the disciplines is the reason that slightly different emphasis may be placed on load development approaches. It is not uncommon to see conditions during the course of a 20+ shot string of fire where it doesn't really matter if your load shoots 0.1 MOA, 0.2 MOA, or even 0.3 MOA; the wind conditions are by far the limiting factor because the speed of the target puller often dictates how fast you can send rounds downrange. Most of these folks will tell you that precision and consistency are key, but most will also acknowledge that pure precision is often not the limiting factor for scores when the conditions are challenging.
With the caveats of proper construction, stiffness, etc., I would also point out that the shooter also needs to think about being comfortable behind the stock. The importance of the "feel" might be more or less depending on your specific discipline, for example whether you use a front rest such as in BR or F-Open, versus a bipod in F-TR. Regardless, a setup that "feels" just right when you get behind it can add an intangible benefit. Within limits, it is certainly possible to adapt to using different styles of stocks. However, there are some extremes past which adaptation isn't going to help. I have always shot F-TR using a traditional bipod (LRA - basically a giant Harris/Atlas with a much wider footprint), loaded quite heavily. I own sled-/ski-type bipods and an eared rear bag, but my preference for tactical-style stocks like the A5, which has a noticeably angled toe, makes it necessary to push the rifle way forward after every shot to bring the muzzle back down on target. I've shot very good scores using these setups, but having to do this every shot during a match absolutely drives me insane. The alternative would be to switch to a stock with a less angled toe and/or a Joypod, but that means using a stock shape/design and/or technique different than what I am used to. So I stick with the bipod and rear bag setup has worked for me in the past. So in addition to the design, construction, and workmanship, there is also the consideration of how good the stock "feels" to the shooter. To some extent you should be able to adapt to a new stock over time, but the closer its feel is to "just right" from the start, the better off you will be. For me personally, chassis systems have never felt right, primarily because I'm used to something different. If at all possible, getting behind the type of stock you're interested in would be a worthwhile exercise. If it feels awkward or uncomfortable to you from the outset, it might not be your best choice, regardless of how well made or functional it may be.