The First Amendment prohibits the Congress (and by extension through the 14th Amendment, the Virginia Legislature) from passing a law respecting an establishmnt of religion.
Here, in fact, the law is demanding that the represenative be from a "religious organization" and also one with a "program for immigrants", that is, a religion with a specific establishment, that is a "program".
I think this law is manifestly UNCONSTITUTIONAL.
Where's the ACLU, and why isn't this puke of a Governor appointing a Sa'ami Noaide to this position?
Actually, you could do better than that. Article VI requires that "no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States." This seldom comes up in litigation, but this seems like an obvious case. Someone really should challenge this.