So for example, in your customizations if you add HTML content (Admin > Customize > Themes > Edit HTML/CSS > Header/After Header/Footer):
<div class="anon-content">
<p>This is test content</p>
</div>
You can then add this to your CSS so that content only shows for anon users:
.anon-content {
display: none;
}
.anon .anon-content {
display: block;
}
If you wanted to go further and only show that content for anon users on the category page, you could use this CSS:
.anon-content {
display: none;
}
.anon .navigation-categories .anon-content {
display: block;
}