how do you clean and whiten white rubber? I have an old Pilates
reformer that has rubber piping around the frame and it is dirty and
badly stained from dirt/abrasion. What's the best way to clean it and
what's the best way to restore the white color?

There are many products that are designed for cleaning and whitening
whitewall tires. I would expect that this would work on anything made
of rubber.

Here's one such product:

http://www.duragloss.com/product.asp?pid=298