Chromate is a relatively strong oxidizer, so it might react with the basins if given enough time and/or some energy. My guess is that it shouldn't be something you'll need to worry about too much.
To more directly answer your question, I would think that chromate could react with stainless steel if you wanted it to, meaning you set up the conditions right. The term 'plastic' can mean all sorts of things, so I can't directly address that question. It would react with some plastics, it may not react with others.
If it is a concern, I would recommend non-reactive glass. It's my hunch that it shouldn't make a difference for what you are wanting to do, but I don't know the details.