How to Reproduce:
- Go to the Search Templates page.
- Switch the style from Style 1 to Style 2 because you want to search for something in Style 2.
- Open the template editor for whatever template and click on Search Templates to go back to the page.
- You'll notice that Style 1 is selected again even though you explicitly chose Style 2 before searching the templates.
It's essentially the same for the Customized Components page.
The only way to work around this and make the style you chose stick is to go to the main Templates page and change it there and then go to Search Templates or Customized Components.