There's a reference in God Emperor of Dune to "spice-plastic" being used on a (pre-Tyrant) reproduction Fremen drum. Presumably the plastics seen in earlier novels are of a similar construction.
As they neared the qanat they heard music from a high entrance of the
sietch. It was an old-style Fremen group—two-holed flutes,
tambourines, tympani made on spice-plastic drums with skins stretched
taut across one end. No one asked what animal on this planet provided
that much skin.
Later books by Herbert's son make more specific claims about its construction and use.
They went together with a security contingent and entered a small
warehouse. Inside, workers moved about like insects in a hive, busily
packaging small books, stacking them into containers, preparing them
for wide distribution across the Imperium. Irulan smelled spice-based
plastic and paper dust in the air, along with the ubiquitous musk of
sweat and the metal tang of machinery.
Winds of Dune
Unswerving, Warrick walked into a common chamber where adolescents
trampled raw spice in tubs; unmarried women curded melange distillate
for the production of plastics and fuel. Against the walls, the whing
and slap of a power loom made a hypnotic rhythm. Other Fremen labored
meticulously on stillsuits, repairing and checking the intricate
Dune: House Harkonnen
Pretty much all of the devices used by the Fremen are specifically referred to as being made of "spiceplastic" in the Dune Encyclopedia
Maker hooks were long, thin shafts of spiceplastic, ranging in length
from 1.35 meters to 2.1 meters, and in diameter from 1.0 to 1.47 cm,
differing no doubt according to the size of the beast and the degree
of skill of their users.
Working examples of the paracompass show almost no deterioration of
the melange-based plastic casing.
The Fremen apparatus used to attract sandworms. An indispensable aid
for travel and often for survival, the Fremen thumper was a
spiceplastic stake pointed at one end and attached to a spring-driven
clapper at the other.
Construction of the normal watertube was somewhat simpler than the
device's sophistication suggests. The compound used for the body of
the tube was melange-based plastic with plyotyl mixed in to provide
the needed flexibility.