Pinned banner doesn't show in front page if 'categories' is the first item in top menu

That is not a pinned banner, but a separate theme. The settings you’re looking at have nothing to do with it, if the banner does not appear on the category page it does so because you’re telling it not to do it with CSS.

How did you add that banner to your site?

Check the banner CSS, you should find a similar line:

.navigation-categories .class-of-your-banner {
        display: none;
    }