Doesn't this kind of direct support of religious schools violate the Constitution?

The short answer is no. Under the Educational Freedom Act the individual student will be subsidized with public funds just as under the current system. The difference is that the parents can use these funds at an accredited private or parochial school. Religious schools, therefore, are not directly funded by the government. This follows the funding approach taken by the Federal Government following World War II when it created the G.I. Bill.  The courts have reviewed and approved this approach. The courts have also reviewed and approved other school choice approaches. Although we can expect that the Educational Freedom Act will be challenged on this and other constitutional grounds there is little or no concern that such challenges will succeed on these grounds. The courts support freedom of religion and freedom of education.