I can speak mostly about the religious left in the United States. There is frankly not a lot written on the topic, at least compared to the voluminous material available on the religious right. What little work has been done on the modern religious left is mostly focused on earlier periods, from the turn of the twentieth century until the 1960s. I would be glad to talk more about that work if you had an interest. There are a few books that might get you started in your thinking about the religious left in the 1980s, though. They are:

McKanan, Dan. Prophetic Encounters: Religion and the American Radical Tradition. Boston, MA: Beacon Press, 2011.

This is a historical overview of the American religious left from about 1800 to the present. It's a useful starting place for further research. McKanan sees the American religious left as having been pivotal to women’s rights, civil rights, and many social reform movements over the course of American history.

Hollinger, David A. After Cloven Tongues of Fire: Protestant Liberalism in Modern American History. Princeton, NJ: Princeton University Press, 2013.

This is a series of essays from a leading intellectual historian about the trajectory of liberal Protestants after the 1950s. Hollinger thinks that the ideas of liberal religious groups informed the broader secular culture, even if they did not flourish institutionally after the 1950s.

Barger, Lilian Calles. The World Come of Age: An Intellectual History of Liberation Theology. New York: Oxford University Press, 2018.

This is a history of the development of liberation theology in Latin Americ and the United States. It covers the popularization of Black liberation theology. Liberation theology was one of the most important theological developments that shaped the American religious left in the 1980s.

White, Heather R., Reforming Sodom: Protestants and the Rise of Gay Rights. Chapel Hill, NC: The University of North Carolina Press, 2015.

This narrative ends in the 1970s but might still be useful. This book argues that liberal religion was pivotal to the rise of the gay and lesbian rights movement on the west coast of the United States. It includes a useful history of the Metropolitan Community Church, a majority gay denomination.