No, SCOTUS is either applying or interpreting the US Constitution, not bowing to the whims of the people. When interpreting the Constitution, especially in cases the Founders never even considered, they can sometimes stretch it pretty far, but given their lifetime appointments they are free from outside pressure. In the decisions that affect the direction of social law and policy, they seem to be looking at trends in case law and perhaps social mores, but I don't think you could call that "public opinion".

And the Civil Rights Act of 1964 (and its add-on in 1968) were DEEPLY unpopular with a lot of US citizens, and were passed with much horse-wrangling by LBJ.