Neither Jews not blacks seem aware of the Klan's great hostility to the Catholic Church. That's because they shared this hostility.
I suspect that the fact that the case supported parochial schools may have been an attempt by Black to cover his tracks. I believe, based on a comment by Justice Jackson in Everson, that Black was more interested in seeding the Everson opinion with his treasonous interpretation of the establishment clause than he was with the outcome of the case.
"The Court's opinion marshals every argument in favor of state aid and puts the case in its most favorable light, but much of its reasoning confirms my conclusions that there are no good grounds upon which to support the present legislation. In fact, the undertones of the opinion, advocating complete and uncompromising separation of Church from State, seem utterly discordant with its conclusion yielding support to their commingling in educational matters. The case which irresistibly comes to mind as the most fitting precedent is that of Julia who, according to Byron's reports, 'whispering 'I will ne'er consent,'- consented.'" --Justice Jackson, Everson v. Board oF Education Of Ewing TP. 1947
Again, in my opinion, Black was more interested in establishing unconstitutional case precedents that could later be regarded as more important that the Constitution.