Their stance on civil liberties has been pretty consistent. All people are equal, and all are entitled to equal protection of their fundamental civil liberties. Their position on border control follows from this: you are entitled to civil liberties because you are human, not because you are an American citizen. There're some pragmatic limitations on this (there's little that the ACLU can do to protect the civil liberties of people residing in China or Russia, for example), but they've consistently fought to extend civil liberties to everyone - even, for example, American citizens of Iraqi descent residing in Iraq.

It's both of the major parties that have inconsistent stances on this, which can largely be summed up as "civil liberties for me, but not for thee". That's why the ACLU tends to get flack from both sides of the aisle. Both parties try to define one group of people as their "tribe" and maximize their own liberties, while defining another group as an outgroup and trying to deny their liberties. And it works: there's nothing quite so motivating as an outgroup. But I'm glad that there are organizations that take a principled, logical stance toward freedom without discriminating against who gets that freedom.