It's actually the other way around. ACLU didn't change their positions in any significant way in several decades now. But the parties and their platforms have changed such that the set of rights and liberties that ACLU promotes now has a "liberal bias", in a sense that it coincides more with the Democratic party platform than it does with the Republican party platform.
But what this tells you is that GOP platform is hostile to civil rights, not that ACLU became partisan.