Why do Christians feel so inclined to subscribe to the conservative party?
Has a major Christian authority taught his subjects that it is righteous to be a Republican?
It's important to check if the Republican party actually has a high appeal with Christians. And if so, with which denominations.
The Pew Research Center has data on this, showing that Catholics actually lean slightly towards Democrats, mainline Protestants lean slightly towards Republicans, but this tendency only becomes prominent with more radical Christian groups.
For 47% of Democrats, Religion is "very important" (vs 69% of Republicans), so the Democratic party seems to have a high appeal to some Christians as well. But we can also see that only 25% of Democrats look to religion for guidance on what is right and wrong (vs 44% of Republicans).
played a key role in the mobilization of conservative Christians as a political force
The NYT notes:
American evangelicals had long steered clear of politics, but with the advent of Moral Majority that was no longer so. “For really the first time in any significant way, evangelicalism becomes interlocked with the Republican Party,” Randall Balmer, a professor of religion at Dartmouth College, told Retro Report.
Important issues were related to selective Christian morality regarding sexuality and women's rights (eg opposition to homosexuality or abortion, but less so to divorce or sexual assault).
I believe there are two main reasons for this, values, and support.
The Republican party, and widely accepted interpretations of Christian doctrine seem to line up, the fact that both things tend to hold tradition in high esteem and long to conserve what is, or what was. Those who tend to value the past tend to side with the Republican party, in this way the Republican party is made up of people that might be older for the same reasons it's made up of people who are more religious.
The Republican party supports the preservation of religious liberties, and in turn, the Christians support the Republican in an act of self-preservation. As humans, we tend to support people that speak on our behalf. You can see this on the flip side with the Democratic party and the LGBT+ community, the Democratic party is outspoken for them and in turn, they support the Democratic party.
TL;DR: It's not so much that Christians support Republicans; it's that Christians find that many people aligned with the Democratic Party are actively destroying what Christians cherish, and the Republicans are the only alternative.
The left tends to think of "rights" in terms of "What should my government be doing for us?", while the right tends to think in terms of "What should my government not be doing to us?".
When it comes to religion, Christians feel that the Democrats are telling them that not only must they accept non-traditional sexual relationships, they must embrace the situation and not be critical of elements of society that promote behaviour that Christians consider inappropriate for themselves. Christians feel they are being forced to do things they believe wrong, and that they are prevented from doing things they think are right.
A committee in the California State Assembly has passed a resolution telling pastors to affirm homosexuality which, for many pastors, would be a violation of biblical beliefs.
Assemblyman Evan Low and three dozen other lawmakers pushed the resolution in the state Assembly Judiciary Committee that's aimed at telling religious leaders in California what they should preach.
E.g. Carl and Angel Larsen own a company that wants to record wedding videos:
According to Minnesota officials, the State’s Human Rights Act mandates that if the Larsens make films celebrating marriage between one man and one woman, then they must make films celebrating same-sex marriages as well. State officials have repeatedly threatened to prosecute expressive business owners who decline to create speech promoting same-sex marriages. And there are steep penalties for violating the law, including payment of a civil penalty to the state, triple compensatory damages, punitive damages up to $25,000, and even up to 90 days in jail.
In one direction, even hearing a word that triggers bad feelings must be prevented, but in the other direction people are forced to not only hear about something, they are forced to participate in it. Groups that express this kind of biased double-think scare many people, regardless of their political or religious views.
Most Christians don't fear the leftist beliefs themselves, or even oppose anyone's right to hold and express those beliefs. Their fear comes from knowing that many on the left want the state to legislate and enforce their specific religious-like views.
So it's not so much that Christians support Republicans; it's that Christians find that many people aligned with the Democratic Party are actively destroying what Christians cherish. And in the USA, when it comes to elections, there are only two choices.