Amusingly, with Mozilla's tracking protection on, Ghostery set to block everything it knows about, Privacy Badger running, private browsing mode, and third party cookies disabled, the Washington Post site not only works, it no longer nags about subscribing.
Btw, for this kind of prompt, one ublock origin features I found very useful is cosmetic filter. I could specify which CSS element permanently to disable by right click menu. I find it useful when I want to watch a specific Facebook video but that annoying Facebook login prompt keeps bugging and it could be triggered by left clicking anything in the page, including expanding comment sections. Though, it's a cat-and-mouse game, and you never know when the countermeasures doesn't work.