Forget that last part (for now).
I just did a test. I added a wysiwyg field to my taxonomy and added my shortcode, which is [home_url].
When I var_dumped this field as follows:
var_dump(get_field('content','{taxonomy}_{term_id}')); exit;
it gives me my home_url.
If I then echo it on my page it produces the same value.
And I didn’t apply any filter or do something extra. This is straight out of the box. So my first guess now is you have something activated (like a filter or so) which stops this shortcode from outputting.
Have you tested this with all plugins deactivated and on a default WP theme ?
