You're only partly right: yes, the ACLU has plenty of money to finance their suits, but did you ever wonder why that is?
It's because there's a law out there that automatically awards them all legal costs when they win!
But of course doesn't pay their opponents costs if (as sometimes happens) the ACLU loses.
Therefore, it's a win-win for the ACLU: if they win, the action costs them nothing, but even if they lose, their opponent has suffered through costly litigation.
THIS law needs to be changed!