There are cases in which the ACLU has defended a number of groups of people, such as the KKK, in order to protect their First Amendment rights. They are willing to protect free speech for any citizen and that includes abortion protesters. The ACLU does not discriminate against anyone, especially based on what they are protesting.
The American Civil Liberties Union is one of those organizations that's easy to hate and vilify until you actually need them. One of the reasons I admire them is that they don't stick to just liberal causes, though of course those are the ones you hear about the most. They've gone to court to help racist groups like the KKK and unpopular groups such as abortion protesters. They are for civil liberties for all.