Seems like Idea and Feature lists should default to the product you're viewing. If I switch products from Product A to Product B, but I had the list filtered by Product A, Product A still displays in the list. Or maybe that’s fine, but when I switch products up top, I assume I’m switching to it on each child page. I’d rather use my master product line to see all products and assume that when I switch at the top, I’m drilling down to only that product for all views.
The list views are customizable global views of data. They remember whatever filters you last set so when you come back to the screen it shows whatever you had pulled up last.
If you select the "Default view" the default view will auto-filter the list to only show features, ideas, etc related to that specific product you are looking at. As soon as you edit anything, it becomes a custom view and the auto-filter functionality is overwritten with whatever you edited. Re-selecting default view will put it back to auto-filter.