Also I believe that Firefox doesn't use the same font resolution as fontconfig. I certainly remember it doing some very baroque unicode fallback as compared to other programs.
I specifically remember writing fontconfig overrides after I felt dissatisfied with some aspect of font rendering in the browser, mostly when it failed to pick up a FOSS drop-in replacement, e.g. Jost* for Futura.
My experience is that Firefox picked up every change to `~/.config/fontconfig/fonts.conf` so far, immediately after I ran `fc-cache -f` and then restarted the browser.
The gsfonts package comes with a fontconfig file that automatically aliases `cursive` to the Z003 font, which is also what the browser shows me.
[0]: https://github.com/ArtifexSoftware/urw-base35-fonts