Many people find that different sharpening tools work better for different types of steel. Some steels respond more favorably to certain types of sharpening tools. As it applies to knife sharpening, for the vast majority, I doubt the question of cross-contamination between stainless/non-stainless is of major concern. 99% of rust issues can be avoided simply by keeping the knives & tools clean and dry. Treat every blade & tool as if it wasn't stainless, and you won't have any issues. Bear in mind, ANY steel will rust, given the right conditions. Even so-called 'stainless' is just a little more 'rust resistant' than so-called 'non-stainless'. It's not rust-proof.
In order for rust to form on any steel, stainless or not, you need (at a minimum) iron and oxygen, in the presence of moisture. Keep the moisture under control, and the rest is pretty much moot. Other things, like salt & acids, can accelerate rusting. Keep everything clean, and that's not much of an issue either.
If cross-contamination was a major issue with knives & sharpening, we'd probably have warning labels on every sharpening tool, cautioning against using on both stainless & non-stainless. There's really not much need to worry about it here.