It's ugly, it's vulgar, and it makes any code less desirable to read. I feel like my eyes are being yelled at for doing something wrong when I read it.
The most common place I see SCREAMING_SNAKES, is when someone uses it to define a constant. At the top of a file. Let's think about that for a second. They took the effort to arrange their code in such a way they can put the constant at the top. (let's assume it had positive outcomes and wasn't a pointless re-factor) now, when I open their code, the first thing that hits me in the face is a stack of SCREAMING_SNAKES! They all kind of meld together - typically, I'll just ignore them and move on to where the real code begins. Then at periodic places throughout the code, I get a SCREAMING_SNAKE to the face, which I probably do want to decipher this time, and hopefully, it's named carefully so I can determine the content of the variable based on the name (entirely different rant.)
It's 2017. We have the good(?) fortune to have hundreds of build tools at our disposal to work around browser caveats and implement half baked specs that make embedding SCREAMING_SNAKES completely un-necessary, a.k.a imports!
In my opinion, take your dirt SCREAMING_SNAKES and move them to a separate file. You can even call that file constants.js if that fits in with your file structure. Export all your constants, then you can import them where ever you need to. (and, they will be proper constants i.e. immutable thanks to the transpiler tasks in your build pipeline.) And guess what, you don't need to make them SCREAMING_SNAKE case to make your point.