I seem to recall the Al Gore (Sr) was one of the Democrat Senators that was fillibustering the Civil Rights Act. I don't believe that the fillibuster had a single GOP member. In fact, on a percentage basis, more GOP senators voted for the CRA than did Dems.
No, it's more complicated.
You gotta differentiate between those who actively filibustered (which did NOT include Al Gore sr, though it did include a majority of the Senators from the confederacy, and did not include any Republicans) ,those who voted to prevent cloture and later voted against the Act (which included Al Gore sr and every other Southern Senator including the single Republican, and a large number of Republicans) and those who voted to prevent cloture at first but later changed their minds after a couple of provisions were taken out, and then voted for the Act (which, together with those who remained opposed, include the majority of the Republican party in the Senate, including the minority leader Everett Dirksen).