$data['appropriate_date'] = "2017-11-15";

// array
array(4) {
  [0]=>
  object(stdClass)#43 (1) {
    ["date"]=>
    string(10) "2017-11-13"
  }
  [1]=>
  object(stdClass)#44 (1) {
    ["date"]=>
    string(10) "2017-11-14"
  }
  [2]=>
  object(stdClass)#45 (1) {
    ["date"]=>
    string(10) "2017-11-15"
  }
  [3]=>
  object(stdClass)#46 (1) {
    ["date"]=>
    string(10) "2017-11-16"
  }
}

e sempre me retorna que não existe

  if(in_array($data['appropriate_date'], $proposal_dates)){
            echo 'a data existe no array.';
        } else{
            echo 'a data nao existe no array';
        }