"Here in CA, most types of clean waste (styrofoam one of the
exceptions)
can be placed (and mixed-in) the recycling bins e.g., all the different

types of paper, plastics, metals, etc. Nothing has been said about
rubber or tire-parts. "

The fact that nothing has been said about tire parts or rubber pretty
much tells you that they don't want them in the recyclables, doesn't
it? I'm sure no one is regularly chopping up tires and putting them in
with the other standard recyclables. And if they did, what do you
think would happen to it when it gets to the recycling facility? Most
likely, it would get chucked into the stuff headed for the land fill.

I also find it interesting that in your area of CA you can just mix all
the recyclables together. It's very unusual to see paper mixed with
glass, cans etc. I would think this would make a big mess to try to
sort out. More typical is to have it seperated:

newpaper
mixed other paper
glass/cans/plastic

And event these typically have some restricitions. For example, glass
means containers, not window glass, and as you pointed out, plastic
means household containers, not styrofoam, etc. Some also require
glass seperated from metals.