rss-club.php

<?php

add_filter( 'pre_get_posts', function( $query ) {
	if ( is_admin() ) {
		return $query;
	}

	if ( is_feed() ) {
		return $query;
	}

	// Exclude everywhere but admin pages and feeds.
	$cat = get_category_by_slug( 'rss' ); // Your "hidden" category's slug.
	$query->set( 'cat', '-' . $cat->term_id ); // Could probably also use `category__not_in`, but whatevs.

	// Now, this would probably not yet exclude the (now seemingly empty) "rss"
	// category from, e.g., the category list widget. (Is that a thing, still?)
	// But doing so would be easy enough, too.

	return $query;
}, 9999 ); // Because who knows what other callbacks are being run.