The source of the confusion is the mistaken notion that the categories “religious” and “secular” are strictly binary, like an on-off switch. It’s true that some things are inherently religious, like a prayer or a church or a Torah scroll. (It would be impossible to make heads or tails of them without reference to their religious nature.) But it’s also true that many things that are not inherently religious are not inevitably secular either: they can be infused with religious meaning through the intention of a believer. A gymnasium or a warehouse has a perfectly secular use but also can be consecrated by worshipers who invoke God’s name there for purposes of worship. Examples of what you might call “dual use,” such things can be at once secular to one person and religious to another.
The most convincing interpretation of our constitutional tradition is that the government may not engage in or pay for conduct that is inherently religious but may accommodate religion when the steps taken to do so are not inherently religious in themselves. The phenomenon of dual use suggests a helpful way of restating this requirement: the state may expend resources to accommodate activities that are religious in the eyes of the believers as long as those activities can still be performed by the general public that interprets them as secular. (link)
This might seem wishy-washy, but actually I think it makes a good deal of sense. In the end, Feldman does come out against public funding for the Khalil Gibran Academy, as well as a Jewish-themed charter school proposed in Los Angeles.