Playing the game of where we stand relative to prior generations of political leanings is an interesting project.
The Democratic party has moved away from union protections, but is still protective of unions. Private unions are a smaller portion of the workforce now. Many people (like Bernie Sanders) claim this is the Dems abandoning the left.
The Democrats are also much less active about trying to establish a single-payer health insurance system than they used to be, so moved to the right.
The party has been more active recently in asserting the rights of LGBTQ+ people and black and Latino people. People view this as a move to the left. Dems (at least this one) often think this is a reaction to greater political winds against these groups, i.e., the Voting Rights Act has been gutted, and there is much more focus on patricularly trans people lately.
Dems continue to focus on "green energy" which is a "left" position, but this isn't much of a change.
Dems have been more supportive of military spending in the Obama and Biden terms than it was during the Clinton administration, and certainly than during the Carter administration. Biden's support for Ukraine has been in line with the traditional hawks' views of national secuirty. So that's a move to the right.
The Dems have been more protective of international trade agreements, which is a move to the right (the unions consistently dislike them).
Since Clinton, the "welfare state" has been significantly curtailed. That's a move to the right. During the 2008 recession and the COVID pandemic both sides spent a lot of public dollars, but given that the W. and Trump administrations spent a bunch of money, it's hard to say that Obama and Biden doing the same thing was an expansion of the welfare state.
Although the Dems continue to have plenty of people advocating for much higher marginal tax rates for the wealthy, as a party they have not done much to make dramatic changes. Biden succeeded in raising some marginal rates, but the Dems seem to have given up on capital gains taxes at lower rates than income taxes, and on estate taxes. Those are moves to the right.
By all accounts, Obama was ready to make a serious move on entitlement spending (Social Security and Medicare/Medicaid). That was a move to the right.
Conversely, Trump says Social Security is off limits, so that's a move to the left.
The Republican Party still wants to diminish the power of the administrative state, although it has gone further to the right on dismantling departments that Nixon set up, i.e., the Dept. of Education and the E.P.A. To be fair, Reagan also didn't like those agencies. Going after the Dept. of Energy is an interesting one: that's primarily the support of nuclear power, which has had more right-leaning support. And the Republicans still want to reduce taxes, primarily through a reduction of the top rates. No change there.
However, the Republican international policy is much more isolationist--is that a right or a left move? I argue that's a move to the right from a historical perspective. It is also a dramatic change from the communist-fighters of the Cold War, and the Middle East policy under Reagan and both Bushes. It could also be viewed as a move to the left--at least in the sense of cutting military spending. Whichever direction it goes, it is a dramatic change from the Republican Party I grew up with.
The Republicans have long targeted affirmative action, but Republicans consistently voted to reauthorize the Voting Rights Act, but that has come to an end. That is a move to the right, as is the attempt to impose heightened voter-ID requirements.
Republicans seem to have given up on LGB issues, but have gone all in on T issues. Move to the left on the former, move to the right on the latter.
Republicans have become much more aggressive about immigration issues. That's a move to the right.
Republicans have abondoned free trade ideology. That is a dramatic change. Is that a move to the right or the left? 30 years ago the Republicans would have called that a move to the left.
On health care, the Republicans seem to have given up on trying to come up with a plan. But maybe that's my jaded perspective. Opposing single payer has remained, but the Obama plan was a variation on a theme that originally came from Romney, and before him (partially) from the Heritage Foundation. So I don't know what to make of that.
Curiously, Trump's frustration with investigations into him and the January 6 incident have resulted in the Republicans turning on federal law enforcement in a way that would make 1960s dems blush. That's arguably a move to the left, but it's hard to separate it from the specifics.
Trump realized a right wing Republican dream of overturning Roe v. Wade, and Republican-controlled state houses have done what they have argued for for many years. No change there, but Trump did de-emphasize abortion in his most recent campaign. Is that a move to the left? Arguably, but I would argue it was coming to grips with political winds as best as possible.