If the ACLU had to take the oath, they would have to stop 90% of their activility (if they were honest, of course!)
Most of us here know the ACLU is not honest. But perhaps what they object to in this matter is that they're being forced to lie if they answer "No" to the oath.
I say, why should they feel any differently about lying to the courts now? Every one of their cases is a lie from the start. Their entire reason for existing is a lie. They were formed by and serve the Master of All Lies.