One way to do it is a bit of a multi-step process.
First, in the view itself under ADVANCED -> CONTEXTUAL FILTERS set up a contextual filter for the taxonomy field you want to filter the view based on (make sure that field is also added to the view's fields.
second, you'll need to add a bit of code to a custom module. You'll want to implement hook_views_pre_view
/**
* Implements hook_views_pre_view().
*
* @param ViewExecutable $view
* @param string $display_id
* @param array $args
* @return void
*/
function MYMODULE_views_pre_view(ViewExecutable $view, $display_id, array &$args) {
$account = \Drupal::currentUser();
// DO A LOOKUP FOR THE USER'S FIELD
$VALUE_FROM_USER_FIELD_LOOKUP = 'SOMETHING';
// IF WE ARE IN THE RIGHT VIEW AND DISPLAY
if($view->id() == 'MY VIEW ID' && $view->getDisplay()->display['id'] == 'MY DISPLAY ID') {
// ADD SOME CUSTOM ARGS TO THE CONTEXT FILTER
$args = [implode("+", $VALUE_FROM_USER_FIELD_LOOKUP)]; //implode on + or some other character? for multi-value contextual filters...
}
}