Passing variables set by widgets

I have a plugin that creates a widget where the user selects a category for display. How can I pass that category they chose to the add_filter() function. Or maybe use the chosen category in the function that I call with the add_filter? (see comment line in CAPS in below code)

add_filter('the_posts', 'post_exclusion', 10);

function post_exclusion( $posts ) {

	if ( is_admin() ) { return $posts; }

		//create an array to hold the posts we want to show
		$new_posts = array();

		//loop through all the post objects
		foreach( $posts as $post ) {

			//for each object get an array of applicable categories
			$cats = get_the_category( $post->ID );

			//create a variable that determins if this post should be included
			//the default is true, i.e. include the post
			$include = true;

			//loop through all the categories applicable to the post
			foreach( $cats as $cat) {

			//if the post is assigned to our undesirable category then do not include it
                        //I WANT TO USE THE CHOSEN CATEGORY FROM THE WIDGET HERE
				if ( $cat->name == 'Testimonials' || $cat->name == 'Listsonly' ) { $include = false; }
			}
			//if we want to include it then add the post object to the new posts array
			if ( $include === true ) { $new_posts[] = $post; }
		}

		//send the new post array back to be used by WordPress
		return $new_posts;
	}