Surely you solved this, but in case anyone else is looking for how to do this:
1) Create a custom.js file inside your theme folder with this code (remember to change IDs with your own):
jQuery(document).ready(function(){
jQuery('#your_select2_select_id').on('select2:select', function (evt) {
jQuery('#your_select2_form_id').submit();
});
});
2) Load custom.js from your functions.php like this:
add_action( 'wp_enqueue_scripts', 'my_custom_script_load' );
function my_custom_script_load(){
wp_enqueue_script( 'my-custom-script', get_stylesheet_directory_uri() . '/custom.js', array( 'jquery' ) );
}
3) Hide the “apply filters” button within your style.css file or the custom CSS box in the plugin’s control panel:
.beautiful-taxonomy-filters-button {
display: none;
}
4) Enjoy! ??