Not everything said by a Gadol (or Chazal for that matter) is meant literally. Just because Rav Shach wrote a letter against an institution does not mean that Rav Shach held that the institution should be closed or not attended by frum Jews.
Rather it may mean that he saw some problem in the institution or flaw which could lead to a problem and felt that a machaa needed to be made to correct the problem or prevent the danger from occurring.
For example: Rav Shach wrote a letter putting a (then new) Israeli Torah institution in cherem and forbidding parents from sending their children to the institution because the institution had secular studies. The RAM that started the institution visited Rav Shach and asked the Gadol whether he, the RAM, should close the institution. Rav Shach said “chas v’shalom,” the institution is needed for many. Rather Rav Shach did not want that such institutions should become the norm and so Rav Shach came out strongly against it.