Open source gpu drivers on Linux clear all allocations the kernel driver hands to userspace. And where it exists, different clients are also isolated from each another through the gpu MMU. On top of that all drivers guarantee that no gpu client can escape the gpu sandbox to general system memory, and on chips where hw engineers didn't provision any useful hw support to enforce this it is done by pretty costly gpu command stream parsing in the kernel.

You can't opt out of these security features on upstream/open source linux drivers either.

Now of course this won't insulate different tabs in chrome since chrome uses just one process for all 3d rendering. But GL_ARB_robusteness guarantees plus webgl requiring that you clear textures before handing them to webpages means that should work too. On top of that webgl uses gl contexts (if available), and on most hw/driver combos that support gpu MMUs even different gl contexts from the same process are isolated.

This really is a big problem with binary drivers, and has been known for years.