  We introduce a version of skein categories which depends on a tensor ideal in
a ribbon category, thereby extending the existing theory to the setting of
non-semisimple TQFTs. We obtain modified notions of skein algebras of surfaces
and skein modules of 3-cobordisms for non-semisimple ribbon categories. We
prove that these skein categories built from ideals coincide with factorization
homology, shedding new light on the similarities and differences between the
semisimple and non-semisimple settings. As a consequence, we get a
skein-theoretic description of factorization homology for a large class of
balanced braided categories in Pr, precisely all those which are expected to
induce an oriented categorified 3-TQFT.
