How to disable saving/changing update date for certain admin users?

A bare-bones version would look something like:

function deny_post_date_change_wpse_131049( $data, $postarr ) {
  $user = wp_get_current_user();
  //   var_dump($user); die; // debugging
  if (in_array($user->ID,array(14,19))) {
    unset( $data['post_date'] );
    unset( $data['post_date_gmt'] );
  }
  return $data;
}
add_filter( 'wp_insert_post_data', 'deny_post_date_change_wpse_131049', 0, 2 );

I expect that in practice you probably want more complicated logic but that should get you started.