WordPress filter to display only root categories and sub categories.

functions.php

<?php

function prefix_get_the_terms( $terms, $post_id, $taxonomy ) {
	if ( 'category' == $taxonomy ) {
		if ( is_category() ) {
			$current = get_queried_object();

			$sub_terms = get_terms( $taxonomy, array(
				'child_of' => $current->term_id,
				'fields'   => 'ids',
			) );

			$terms = array_filter( $terms, function( $term ) use( $sub_terms ) {
				return in_array( $term->term_id, $sub_terms );
			} );
		} else {
			$terms = array_filter( $terms, function( $term ) {
				return 0 === $term->parent;
			} );
		}
	}

	return $terms;
}

function prefix_template_redirect() {
	add_filter( 'get_the_terms', 'prefix_get_the_terms', 10, 3 );	
}

add_action( 'template_redirect', 'prefix_template_redirect' );