Should government be permitted to condition its subsidies on adherence to non-discrimination conditions? It depends. Government in my view should be able to refuse to subsidize those organizations that discriminate on the basis of race or sexual orientation even if the basis for the discrimination is religious.
It similarly should be able to refuse to subsidize those organizations that discriminate on the basis of religion except for religious organizations. If non-religious organizations discriminate on the basis on religion, there is reason to think the discrimination is odious. If a religious organization engages in such discrimination re membership or re its leaders, the government is foreclosed from thinking that this is odious. This would not necessarily mean government could not draw a line somewhere regarding its subsidies for a religious organization's religiously-based decisions regarding employment (though it might).
Note that these issues were not presented in CLS v. Martinez which merely held that a law school need not subsidize an organization, religious or otherwise, that was not open to all students.