If we’re talking about, say, supporting LGBT people, then yes. Gay marriage was not considered ideal even in the LGBT community, in the 1960s, while today it’s the law of the land.
However, if we are talking about things beyond respecting people’s race/sex/etc, things have definitely moved to the right. No democratic candidate has supported anything like Johnson’s “Great Society” in decades. Obamacare is to the right of Nixon’s healthcare proposals.
Society has not simply moved “To the left” or “To the right,” because while “Left” and “Right” can describe general philosophies, they are not immutable and objective points on a line. The general philosophy of society has changed in such a way that it’s moved ‘to the left’ on aspects of social egalitarianism (Neither Republicans nor Democrats today would ever run on an explicitly segregationist platform as Wallace did) but ‘to the right’ on aspects of government spending, economic policy, and some would argue national defense. (I would argue our defense philosophy to be neither “Left” nor “Right,” but either way we certainly are more WILLING to get militarily involved. We used to require a direct idea of what threats could come — Hence Vietnam on the grounds that it would endanger the US for Vietnam to fall to Communism — While now we will support military engagement for “Defending Civilians,” and thus are involved in combat against both Assad and ISIS.)