You can do this by using hook on taxonomy insert and update inside a custom module.
Here is a sample of code (needs refactoring/cleaning/checking but that's a start and it works for me) :
function custom_module_taxonomy_menu_insert(&$item) {
//load taxonomy to access fields
$tax = taxonomy_term_load($item['tid']);
//get your field display (here i called it field_status)
$display = isset($tax->field_status['und'][0]['value'])?$tax->field_status['und'][0]['value']:'';
//check your value
if($display == 0) {
//I don't want to display this element
$item['remove'] = TRUE;
return $item;
}
}
function custom_module_taxonomy_menu_update(&$item) {
//IDEM without comments
$tax = taxonomy_term_load($item['tid']);
$display = isset($tax->field_status['und'][0]['value'])?$tax->field_status['und'][0]['value']:'';
if($display == 0) {
$item['remove'] = TRUE;
return $item;
}
}
[Edit to add some details]
The menu will not update automatically, you'll have to save/update your terms to update the menu (hook_taxonomy_menu_update). For new terms, it's going to work automatically (hook_taxonomy_menu_insert).