Custom Meta Box (SELECT2) Not Saving Taxonomy Terms

First of all you saved the the terms value in a post meta table and not following the wordpress conventional method.

To make it connect with default category with that post you need to modify your save_post action. Check the modified code. 

add_action( 'save_post', 'rudr_save_metaboxdata', 10, 2 );
function rudr_save_metaboxdata( $post_id, $post ) {

    if ( defined('DOING_AUTOSAVE') && DOING_AUTOSAVE ) return $post_id;

    // if post type is different from our selected one, do nothing
    if ( $post->post_type == 'post' ) {
        if( isset( $_POST['rudr_select2_cat'] ) )
        {
            wp_set_object_terms($post_id, $_POST['rudr_select2_cat', 'category', false) ;
            update_post_meta( $post_id, 'rudr_select2_cat', $_POST['rudr_select2_cat'] );
        }
        else
            delete_post_meta( $post_id, 'rudr_select2_cat' );
        if( isset( $_POST['rudr_select2_tags'] ) )
            update_post_meta( $post_id, 'rudr_select2_tags', $_POST['rudr_select2_tags'] );
        else
            delete_post_meta( $post_id, 'rudr_select2_tags' );
    }
    return $post_id;
}

Please check wp_set_object_terms() for reference.

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