I think some key words for you to research would the ‘southern strategy’. I feel like people are giving you trite and naive answers. The material foray into politics began under Reagan and started as the ‘southern strategy’, which was a strategic effort in the religious south to move people to the right, but also to reshape what Christianity was and is defined as in the US. This strategy did as much to reshape religion in the US as it did politics, and Reagan, arguably, represented the culmination of that strategy to establish the modern political hedgemenoy we live under. Effectively, our politics haven’t really changed in the US since then (not materially in paradigm or structure). This is also when neoliberalism became the defacto politic of western governments.

It’s really too much to unpack in a response, and I’m on my phone so I can’t hand you great sources, but starting by googling southern strategy, and looking back to the late 50’s.

Further reading:

• Reagan tied Republicans to White Christians and now the party is trapped, Washington Post
• Religion and Right-Wing Politics: How Evangelicals Reshaped Elections, New York Times
• Moral Majority, Wikipedia