How to select a template for a custom post type?

According to the WordPress template hierarchy, a custom post type ‘my-cpt’ will first try to use single-my-cpt, then single.php and then index.php. The above issue is not caused by templates – indeed 404s are used when the content, not the template, cannot be found.

You are using a custom rewrite:

'rewrite' => array( 'slug' => 'members' )

For WordPress to recognise this you’ll need to flush your rewrite rules by visiting the Settings > Permalink page.