RSS/XML of all Categories and/or Tags

Question

Is it possible to get an RSS / XML feed of all WordPress Categories and/or Tags?

I've searched the Codex, which was very helpful in giving examples on how to access specific, individual RSS feeds, but have not been able to find any source on how to display all Categories of a site.

Using examples from the Codex, specific Categories can be found with the following structure:

example.com/category/categoryname/feed

I'm looking for something along the lines of:

example.com/category/*/feed

OR

example.com/categories/feed

Any thoughts? Solutions? Suggestions?

---

EDIT: I'm not looking for a feed of posts, rather a feed of all actual categories or tags. Ideally, this feed would contain only the categories themselves, no specific post data. Using the categories in the feed, however, I'd be able to then gather posts as needed by looking at each of the categories specific RSS feeds.

An example of what I'm looking for would be a feed that returned the following list:

• Category 1
• Category 2
• Category 3
• Category 4

Iterating over that, when needed, could give me the posts for each.

Answer 1

Demo plugin for JSON export:

I'm not sure the RSS feed structure suits your needs, for example taxonomies and terms don't have any dates for the public date field. So here's an example how you can retrieve all the terms for a given taxonomy:

/** 
 * Plugin Name: WPSE - JSON export all terms for a given taxonomy. 
 * Plugin URI:  http://wordpress.stackexchange.com/a/151908/26350
 * Version:     0.0.1
 */ 

add_filter( 'query_vars', function( $qv ){
    $qv[] = 'wpse-export-taxonomy';
    return $qv;
});

add_action( 'template_redirect', function(){

    $tax = get_query_var( 'export-taxonomy' );

    if( ! empty( $tax ) )
    {
        if( taxonomy_exists( $tax ) )
        {
            $data = get_terms( sanitize_key( $tax ), 
                array( 
                    'hide_empty' => true,
                    'orderby'    => 'name', 
                    'order'      => 'ASC', 
                ) 
            );

            if( count( $data ) > 0 )
                wp_send_json_success( $data );
        }
    }

    // Error:
    wp_send_json_error();

} );

where you can modiy the get_terms() arguments to your needs.

Usage Examples:

Categories export:

http://example.com/?wpse-export-taxonomy=category

Post tags export:

http://example.com/?wpse-export-taxonomy=post_tag

Custom country taxonomy export:

http://example.com/?wpse-export-taxonomy=country

The category export could look like this:

{"success":true,"data":{
"0":{"term_id":"65","name":"animals","slug":"animals","term_group":"0","term_taxonomy_id":"75","taxonomy":"category","description":"id:65","parent":"0","count":"5"},
"1":{"term_id":"61","name":"birds","slug":"birds","term_group":"0","term_taxonomy_id":"70","taxonomy":"category","description":"id:61","parent":"65","count":"8"}
"2":{"term_id":"13","name":"falcons","slug":"falcons","term_group":"0","term_taxonomy_id":"15","taxonomy":"category","description":"id:13","parent":"61","count":"3"}
}}

I hope this helps.