So its neither a Linux nor an open source driver problem. Maybe your hardware is in fact not up to the job or you need to install some updates ;-)
Btw. I also tested chrome and as long as I run it with default settings I get around 3-5fps, but when I activate #ignore-gpu-blacklist in chrome://flags it reaches 60 fps there too.
The code copied to a pastebin: https://pastebin.com/f4uFYMzy
Recorded webm with the shadertoy-integrated record tool: https://gfycat.com/CrazyMassiveBluewhale or https://webmshare.com/vPx9d (sorry for having the tab in the background while recording :P)
But it worked fine on my Debian Stretch laptop with Intel integrated graphics. MED was pretty slow, but VERY_LOW and LOW detail levels were fine.
60fps.