What were/are the political goals of the Religious Right?

The Religious Right has played a prominent role in American politics since the late 1970s. In particular, it has developed into a powerful, vocal element within the Republican Party. All of the various political objectives of the Religious Right are in some way related to a specific brand of Christianity, one which embraces the core tenets of both evangelical and fundamentalist Protestantism.
When it first emerged on the political scene in the 1970s, the Religious Right saw the Cold War in terms of an apocalyptic struggle between the forces of good and evil. This Bible-based approach to foreign affairs found expression in a famous speech by President Reagan in which he described the Soviet Union as "the evil empire." Reagan and his supporters of the Religious Right saw the USSR not just as a rival power but as the embodiment of evil, the chief promoter of atheism in the world. Though Reagan later adopted a more pragmatic approach towards dealing with the Soviets, his fundamental worldview remained similar to that of the Religious Right.
The Religious Right has also been at the forefront of attempts to abolish, or at the very least restrict, abortion. The landmark Supreme Court ruling in Roe v. Wade (1973) spurred religious conservatives into action, leading them to become more organized and better funded in their attempts to get the decision reversed. To date, conservative activists have not been successful in their endeavors, but they have made progress at the local level as a number of state legislatures have severely restricted access to abortion as well as contraception in general.
The issue of abortion highlights the fact that the main focus of the Religious Right has always been on social policy. In particular, religious conservatives have been keen to halt what they see as the decline of the traditional family. To that end, they have been very active in opposing the legalization of same-sex marriages and same-sex adoptions. The conception of marriage which they advocate is based upon an understanding of the Bible that sees homosexuality as a sin and marriage as a special gift from God that can only take place between a man and a woman.
https://oxfordre.com/religion/view/10.1093/acrefore/9780199340378.001.0001/acrefore-9780199340378-e-97