The way it is now, ClothVertex->mass is used once in
cloth_from_object / do_init_cloth, where SIM_cloth_solver_init /
SIM_mass_spring_set_vertex_mass are called and set up masses in
Implicit_Data.
The masses from Implicit_Data are accessed in many places, so it would
be mandatory to have these masses kept up-to-date (and even then I am
unsure if the solver was designed to work with this animated? Or if
there are assumptions about this being stable across the sim?)

Seems possible to update ClothVertex->mass every step in
do_step_cloth, however it seems more involved to update the masses in
Implicit_Data there as well?
Also not sure about possible scenarios to check/verify this would
actually work as expected in all scenarios?
(left commented in the patch, to be removed prior to commiting)

So propose to remove the (broken/not implemented) animation capabilities
on the property instead.