I have many fixtures with rubber gaskets that have turned into solid shattered plastic or some sort of goo substance that is likely toxic...

I also have a street light or two with white fiber gaskets. Does anyone know of a source for sheets of that particular fiber type gasketing material? I would like to use materials that have more longevity.

That goo is unlikely toxic other than being just black and sticky)

Silicone is considered more stable. Probably you are talking about some reinforced silicone rubber?

Dunno what gets created from old age, but from high heat e.g. fire many rubbers tend to turn into goo containing hydrofluoric acid. Not that much toxic by itself, but aggressive etching thing, may cause etch burns...
So mainly when really goo-ish, better handle it with gloves and treat it like it really may "bite"...

Not many rubbers fortunately, but only fluorinated elastomers like viton. Otherwise, until forcibly burned, viton is extremely stable and will not decompose under normal environment to any sensible amount of HF. It is even used widely in gaskets in sub-micron vacuum systems for this reason. So please do not spread this unfounded scare! Other rubbers decompose to some partially oxidated hydrocarbons, which remain pretty benign. Chlorinated rubbers may give some trace HCl but I bet it will evaporate and dissipate quickly and is not toxic in such minor amounts, your stomach sure has much more