That's not a lock that they were in fact "conservative," but four of them were put on the court by Nixon, and regarding Blackmun, "The Justice Department including future Chief Justice William Rehnquist investigated Fortas at the behest of President Richard Nixon who saw the idea of removing Fortas as a chance to move the Court in a more conservative direction, and Attorney General John N. Mitchell pressured Fortas into resigning." https://en.wikipedia.org/wiki/Abe_Fortas
So four were appointed by Nixon, who specifically had in mind moving the court to a more conservative stance. The fact that he failed miserably with Blackmun notwithstanding, the only thing that can honestly be said of the court at the time is that it was less conservative than courts that followed, not that it was liberal.