.......... though possibly with asbestos as a filler in the plastic. If so, quite inert unless you go at it with a grinder. It is probably asbestos fibres which give it the strength you describe.
Apologies for people who may know this already but here are a few common places that we as plumbers are likely to come across asbestos:
Compressed fibre gaskets for immersion heaters, pumps etc
Pipe lagging and cement pipe insulation
Asbestos sheet roofing
"Galbestos" or "Robinsons Protected Metal" corrugate (this is a kind of corrugated metal cladding coated with asbestos in bitumen commonly used on the outsides of commercial and agriculatural buildings prior to the 1980s. It really is everywhere on old industrial estates, factories, farms and warehouses).
Cement fibre flues and chimneys
Boiler lagging and packing, boiler insulation
Fireboard panelling between rooms or in place of plasterboard, and other forms of fire protection.
Drywall compounds
Felt roofing
Plaster
Cement Roof tiles, simulated roofing slates
Old vinyl "lino" type flooring (asbestos was used as a filler in the plastic)
Cisterns (as mentioned) and toilet seats
Loose fill asbestos between floors
Arc shields in electrical switchgear.
"Artex" textured walls and ceilings
Ceiling tiles in commercial and domestic premises ("Asbestolux" for example)
Fibre cement for tile backing in wet areas.
Fibre cement rainwater goods and soil systems
Trivia - there are 6 types of Asbestos:
Chrysotile (white)
Crocidolite (blue)
Amosite (brown)
Anthophyllite
Actinolite
Tremolite
NB you cannot determine the material by colour other than its raw form unless you look at it under a microscope.