The 1st Amendment prohibits a State from establishing an official religion. The use of tax money to transport parochial school students constituted State assistance and tacit endorsement of religious instruction. Therefore, using tax money to transport parochial school students violated the Establishment Clause.
The 1st Amendment, in addition to prohibiting the establishment of a State religion, also prohibits actions which prevent the free exercise of religion. To withhold assistance to parents for the transportation of their children to parochial schools would be to discriminate against parents of Catholic school children and thereby violate the Free Exercise Clause.