Without bugs in the driver, even bad behaviour from the browser shouldn't bring the whole machine down.
Graphics drivers are sadly famously buggy, and occasionally the hardware is buggy too, and the driver needs to work around those bugs in the hardware, and occasionally the users hardware specifically is broken in some way, and then there's no winning.
It's probably true that Firefox has less workarounds for buggy drivers hardcoded into it than Chromium, but in the end the blame is on the driver, and if they had blacklisted your driver the likely "improvement" is you'd no longer have any hardware accelleration, which is not exactly a great result - the real fix needs to be better drivers that don't crash the system for no good reason.
And no problems with websites either. I don't even have Chrome or any chromium based browser installed.
To use software WebRender, set about:config pref “gfx.webrender.software” = true. To use software WebGL, set "widget.dmabuf-webgl.enabled" = false. To use software video decoding, set "media.ffmpeg.vaapi-drm-display.enabled" = false.
If those settings do avoid the crashes, please file a bug report in Bugzilla with a copy of your Firefox's about:support information. Perhaps there is a GPU driver bug that Firefox needs to work around.
If file a bug report in Bugzilla with a copy of your Firefox's about:support information, Firefox developers can work around the buggy GPU driver so other users don't experience the driver crash.
(And one of the PCs it's on runs a GT 710 with now outdated drivers)
I can't remember a single time when it last crashed on me in the last 2 years on both operating systems.