IE probably never
IE is a dead product, it'll probably stay doing what it's currently doing unless there's some major security issue forcing Microsoft to issue a special security update to disable CN validation.
Firefox already there
Firefox already no longer recognize CN for new certificates signed by public PKIs, (deadline was anything issued on/after 2016-08-23) but still allow fallback to CN for non-built in CAs. Since Firefox is an open source product, for items like these, removing CN support likely will require a volunteer that actually goes forward to provide a patch to implement the removal, and such patch likely will only get merged if retaining any CN support is preventing some other major improvements to Firefox or the web/PKI infrastructure as a whole. There's really no big hurry for this removal, as keeping it around doesn't seem to prevent anyone from doing what they need to do at the moment, and the current solution of differentiating built in and imported certificate seems to satisfy Firefox's users for the moment.
Edge and Safari are a Microsoft's and Apple's products, keeping or removing support likely will depend in their respective commercial influences.
Further reading/tracking: ChromeStatus
So far, according to ChromeStatus: Support for commonName matching in Certificates, there doesn't seem to be any public communication from Microsoft and Apple for this topic.