Right now, if I try to visit any page on English Wikipedia, I get a JS exception thrown:
[Exception... "Persistent storage maximum size reached" code: "1014" nsresult: "0x805303f6 (NS_ERROR_DOM_QUOTA_REACHED)" location: "<unknown>"]
This is despite the fact that I currently have nothing in localStorage for English Wikipedia and my localStorage quota is set to the default (5 MB).
I think what's going on is that Firefox is sharing localStorage space across all wikipedia.org sites, and since I have several ~1 MB MediaWikiModuleStores from other Wikipedias, it doesn't have room to store one for en.wiki. See https://support.mozilla.org/en-US/questions/963825 for someone else who noticed the same problem in Firefox but for a different website.
One possible semi-solution to this bug is discussed in bug 64721. Even if the size of MediaWikiModuleStore was reduced, however, you could still run into this problem if you visit enough Wikipedias.