Regardless of how you think the hot button issues of the 1960s and 1970s should have been addressed, you will find Republicans and Democrats on both sides. 
You will find Republican and Democratic supreme court appointees opposing school prayer, forcing school buses to drive across town, saying the pledge of allegiance isn't mandatory, and saying that women have a right to abort their babies. And you will find elected officials of both parties opposing those stances.
In a few very particular cases, you can say that the parties switched sides, especially in the South.  But it's more correct to say that there was a great ideological sorting that peaked in 1994 and continues to drive politics today. So that where you used to find members of both parties on both sides, now you hardly ever find a member of a party who disagrees with their party about one of these issues.


There is still some hope that the great Trump Disruption will break apart the ideological homogeneity of each party to some extent, but Trump still doesn't recognize the opportunity that his popularity affords him to break the sclerosis in the system.  He could be using his popularity to create a coherent deviation from Republican dogma, by endorsing candidates who agree with him on certain key issues, but so far his only strategy seems to be endorsing based on personal loyalty.  And the value of his endorsement is pretty low now, especially compared to how valuable it was in 2018 or 2020.

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