I would actually modify slightly and say that it does matter, in terms of preparation for the LSAT and law school. The LSAT is a test of critical and logical thinking, and law school is big on those skills plus a lot of writing. Traditional liberal arts and sciences majors tend to have those more heavily in their curricula than professional majors like business do.
The solution, though, is simply to ensure that you take courses that will improve your writing ability and your ability to think critically and logically. Even if you major in business, minoring in political science and seeking out writing-intensive classes can do the trick.