How do I toggle list/grid view on section index page without affect category filtering
If I don't misunderstand anything from your question, you're basically looking for a way to pass data with a link, in your case the toggle state, which is responsible for the grid / list view.

There's multiple ways to do that. See Brad's short but precise answer on an related question.

You said that you're preferably looking for a way that doesn't reveal the toggle state in the URL. I can understand the thinkings behind that, but keep in mind, that this is the only way one could save the site or post a link to someone else with the information included.

Another idea: Most sites probably use Javascript for such a toggle (I've seen many Wordpress themes with such a feature). But you'd still need to save the state somehow or completely AJAXify the relevant pages.