Starbucks is testing a new cup. Here's what's different
https://edition.cnn.com/2020/03/09/business/starbucks-new-cup/index.html
Like this example, there are many kinds of components which are recyclable, but cannot be recycled. That's because they are not separable from other components which are not recyclable.
So, it's important for manufacturers to design products so that people can easily separate recyclable components.