In the short to medium term, Netflix, etc. will just fallback on delivering streams through Silverlight of Flash. That's what they do know and those plugins will keep working. There's precedent for this in the way that many websites would deliver H.264 encoded HTML5 videos to browsers that supported those, but used Flash when Firefox didn't support H.264.
In the longer term, Silverlight is abandoned and Flash is on its way out. I think it's unlikely that Firefox holds out against EME in the long term, but it could be that it slowly gains a reputation for being bad for many streaming sites. The Flash fallback is buggier and less featureful than the streaming in other browsers, maybe slower as well. At some point, people upgrade their computers and find it hard to get a Flash plugin that works and so they eventually give up and switch browsers.
I'm not sure how technically possible it is, but another option is that Netflix and similar companies will write their own plugin for Firefox which supports DRM. Presumably they will try to make a plugin which is not a platform like Flash, but only serves the purpose of doing the DRM. An equivalent, but probably techincally superior, option is to put the DRM into an asm.js blob.
Some people in this thread believe that the lack of support for EME will put pressure on media companies non-DRM streaming options. This strikes me as wishful thinking. In the short-term, the existence of Flash and Silverlight fallbacks mitigates the pressure on Hollywood and streaming providers. Again, see the H.264 story. In the long-term, Hollywood's smart enough to realize that if there exists a DRM solution for Firefox today, then it will be technically possible in the future as well.
That's why I don't see the point of boycotting EME. If it could plausibly lead to DRM-free streaming options, that would be an improvement, but I don't believe it will happen. On the other hand, from a binary blob perspective, EME plugins are strictly better than NPAPI plugins, and second, users who don't want DRM can always not use it. All boycotting does is reduce the options for users who are willing to accept DRM.