Keeping kids out of religious homes is exactly what these social engineers want.
I think the smart thing to do is sign the statement, then continue to parent in the way you feel is best.
People of Faith such as these will most likely have a difficult time with such a plan, as it is dishonest, even though it would be done for a worthy goal.
Also, if a Government agency were to direct them to involve themselves in a specific homosexual oriented activity and they were to refuse, prosecution would be likely.
I don't get the impression that these good people are made of money, and so an extended incarceration coupled with a massive court challenge is probably not something that they would be able to pursue.
However, it is not a Christian thing to do to claim you will do something knowing full well that you will not. That is likely why this couple didn't just go that route.