Unlike powder, primer makers change their products periodically without telling anybody. I understand Winchester thinned some of their primer cups out at one point to make them more sensitive. They took the nickel plating off a few years ago, claiming it was for that purpose. I guess they were having ignition complaints. I've seen a couple of places rate them as "soft" now, where that did not used to be the case.
As to the AR, specifically, it does have a floating firing pin and it will put small marks on primers on closing that you can see if you eject them without firing. So, even though it is less prone to slamfire than the Garand and M14 and various foreign-made self-loaders, it still is a concern. Manufacturers seat primers 0.003"-0.005" below flush with the case head, and that's what you want for the AR. In the past I've run lots of the "soft" Federal primers through my Garand and M1A and AR seated in this way with no issues. It is high primers that are the main cause of slamfire trouble, though out-of-tolerance gun parts can cause it, too.
If you have the Forster Co-ax press, it's built-in primer seater is the only one made (AFAIK) that forces a primer to a fixed 0.004" below flush regardless of other considerations. Even Forster's own Co-ax bench priming tool does not do that. I often use a hand priming tool while sitting in front of the TV to get primers into the brass. That lets me feel for bad primer pockets, among other things. But when I load for the service rifles, I then additionally run them through the primer seater on the Co-ax press as redundant seating depth insurance. That is quick when the primers are already in place and don't have to be placed into it one-at-a-time.
Seating primers to the bottom of the pocket is sometimes not enough, due to brass tolerances. Federal specifically recommends that their small rifle primers receive 0.002" of crush beyond touchdown with the bottom of the primer pocket and 0.003" for large rifle primers for best performance. This crush sets the primer "bridge" correctly; that is the distance between the anvil and the bottom of the cup the pellet is squeezed down to. This approach is validated in principle in the Precision Shooting Reloading Guide, where one of the authors points out he can get almost any rifle's velocity ES down to about 10 fps, but when seating the primers far harder than is normally thought best. They work most consistently with a pre-load.
The bottom line is the WSR primers should not be an issue in the AR if seatd properly. Indeed, Glen Zediker said ten years ago that he often purchased factory primed Winchester brass and used it as-is in the AR with good success. That may precede the changes by Winchester to make their primers more sensitive, but I went through a bunch of those factory primed cases with brass-colored primers in my AR about six years ago or so (haven't seen them available for a time). I had no issues with them at all. Just get the primers correctly below flush, and you should be fine.