The giant Southern Baptist Convention, the largest Protestant denomination in the country with around 16 million members, is set to elect a new president next month. The incoming president, to be chosen from three nominees in succession to the widely respected Arkansas pastor Ronnie Floyd, will be elected next month. He will be expected to serve two one-year terms.

Baptist Press has helpful interviews with all three candidates, having asked them the same three questions. Their answers to one of these questions are revealing, not just in what they say about the individuals concerned but in the signals they send to the denomination.

Highly conservative theologically, SBC churches and pastors have been caught up with other US evangelicals in the painful unfolding of the Republican primary nomination. Like other evangelicals, they have been torn between supporting Ted Cruz, impeccably evangelical but divisive and unlikeable, and Donald Trump, religiously dodgy but a masterful player of the populist game.

In their resolute opposition to same-sex marriage, lavatory accommodation for transgender people and abortion, they have placed themselves firmly on one side of the 'culture war' in America. But realistically, the ideologically opportunist Trump is not one of them and even if elected he will not use precious political capital backing them. Their worst nightmare, a Clinton presidency, is the more likely outcome. And social forces in the US are inexorably driving a liberalising agenda whoever is in power. The future for die-hard conservative activists looks bleak. So what will be the tone of public pronouncements from the SBC during the next two years, and who is best placed to detoxify the evangelical brand?

Baptist Press asked several 'in-house' questions of the candidates. However, the most revealing is its final one: "What do you see as the key moral issues of our day, and how can the SBC president represent Southern Baptists as America increasingly moves away from Judeo-Christian values?" Their answers reveal quite different takes on the question.

For Tennessee pastor Steve Gaines, it's clear: "The three key moral issues in our day are abortion, sexual immorality." On abortion, he says: "We must never waver regarding the fact that the Bible teaches that life begins at conception. Every unborn child is an eternal soul."

On sexuality, he says the culture is "morally confused" and says the denomination "must advocate for biblical marriage". "The only marriage Jesus affirmed was heterosexual, monogamous marriage – one man married to one woman for life. God created males to be males and females to be females," he says. "Gender is biological, not psychological."

On the other hand, for Louisiana pastor David Crosby, "The greatest moral issue is our flagging love for the lost and dying around us." He too addresses race: "Jesus introduced race in His story of the Good Samaritan in order to make it abundantly clear that love of neighbour involves loving people across ethnic, economic and cultural barriers."

However, taking a strikingly different line from Gaines, he says: "I am less concerned with the moral drift of the culture than I am with the moral drift of people who call themselves Christians. If we do not look like Jesus in our behaviour, we will certainly not sound like Jesus nor represent Him faithfully in our world."

The third candidate, JD Greear, is pastor of the 10,000-member Summit Church in Raleigh-Durham, North Carolina, the state at the centre of a major row over anti-transgender laws.

However, Greear too is nuanced in his reply, seemingly unwilling to make this front in the culture war a main point. He says: "Antagonism toward Christianity is growing, but this is no time to despair. The early Church didn't grow exponentially because the government was behind them, but because they trusted the Spirit and proclaimed the Gospel boldly.

Thus, while we will continue to advocate for religious liberty, we must also live as the counter-cultural people of God, a unique community where the fragrance of Christ is sweet and distinct. The darker our culture becomes, the brighter the light of the Gospel shines forth."

All of these men are, by UK standards, highly conservative theologically – you don't even get nominated for the SBC presidency if there's any doubt of your orthodoxy. This means, for instance, no women in ministry, (probably) young-earth creationism, biblical inerrancy and absolutely no tolerance of homosexuality or acceptance of transgender behaviour. In strictly theological terms, there's probably no difference between them on social issues.

However, it's possible to discern differences in tone between their public statements to which messengers to the SBC gathering in June will be highly attuned. And while a single individual will have only a limited influence on the churches and pastors of a 16-million-strong denomination, it will send a signal about the kind of face the SBC wants to present to the world. Will it be an uncompromising rejection of Obama and all his works? Will the incoming president continue to use the language of moral decline, judgment and resistance? Or will he attempt to shift the denominational preoccupation with public sexual morality and seek to speak more widely into American culture?

There's no doubt that at the moment evangelicalism has an image problem, in good part because of the bitterness of the Republican primaries. So toxic is the brand that Russell Moore, head of the SBC's Ethics and Religious Liberty Commission, said he had stopped calling himself one. "The word 'evangelical' has become almost meaningless this year, and in many ways the word itself is at the moment subverting the gospel of Jesus Christ," he said in a Washington Post article.

Can the SBC begin to face up to the task ahead of it in reclaiming the word when it's become associated, as Moore says, with "everything from authoritarianism and bigotry to violations of religious freedom"? Time will tell, but the election of its next president will give some sort of indication.

Follow Mark Woods on Twitter: @RevMarkWoods