This is not the webkit browser accessed through Facebook. This is starting from the regular Safari browser.
I subscribe to the Boston Globe (online only) and NYT (online only). If I were to subscribe to a third newspaper, it would almost certainly be WaPo. But that surely will not happen as long as it has this problem.
ETA: R. points out that if you use "reader view" (url line to the left, a bunch of lines representing text), the problem is gone. Also, if you scroll well below any ad being visible, the problem is gone. The problem appears to be when any part of any ad (or at least a motion ad) is visible on the screen.