The Kentucky county clerk who spent time in jail for refusing to issue marriage licences to same-sex couples became an icon for conservative evangelical Christians in the US. But can we accurately call her a Christian? Kim Davis proclaims Jesus as her Lord but does not believe in the Trinity. So does that count?

How do you prove you are a Christian? Is it by what you believe? Or is it by what you do? Or is it neither and you are a Christian just if you say you are a Christian?

Who is in and who is out has always been a fundamental question for religious groups. The early Church frequently changed the parameters as "orthodoxy" was gradually decided over the first four hundred years. Athanasius of Alexandria was exiled several times as a heretic for his opposition to Arius in the fourth century. Eventually however orthodoxy shifted and it was Arius who was declared a heretic and Athanasius heralded as a foundational Church father.

The question of who was and was not a Christian was raised again at the Reformation. For all his early attempts at holding the Church together, Martin Luther ended up labelling the Pope an antichrist and a heretic – in his view the Pope no longer counted as a Christian.

And the question is live again today, especially within Islam. Who counts as a Muslim? Is ISIS Islamic? David Cameron has repeatedly said he thinks ISIS is a "perversion of a great religion" and "no reflection of the true nature of Islam". But on Wednesday the BBC's head of religion reignited the debate when he said although it was "uncomfortable", ISIS preached an "ideology based on some form of Islamic doctrine". "They are Muslims," said Aaqil Ahmed.

It is not just Islam that faces such complex issues today. The question of where to draw the line between who is in and who is out is one for Christians as well. What about the Ku Klux Klan (KKK)? Are they Christians? Or the Lord's Resistance Army (LRA) in central Africa? Or Westboro Baptist Church? All these groups claim to be Christian. So is that enough to make them Christian or is there some objective test which proves they are not?

It was a question fundamental to the campaign by Richard Dawkins and the British Humanist Association (BHA) to encourage people to tick the "no religion" box on their census. Dawkins wanted more specific questions on doctrine to identify whether people were really religious.

"If you really, really want to know whether people are religious in the true sense – the sense that everybody understands about religion – ask a specific question: 'Do you believe Muhammad rode on a winged horse?' something like that," he told the BBC.

In response Paul Bickley from the think-tank Theos said it was wrong to judge how devout someone was and say if they didn't practise their faith then they were out. "You can't say, 'If you don't practise, you're really a humanist, please tick the 'No religion' box'. I think that's to go too far," said Bickley.

These two views broadly encapsulate the two approaches to this question.

The first is to say you are only a Christian if you adhere to certain doctrines. There might be some obvious characteristics that mark out Christian belief such as the Trinity, that Jesus is God, that he died for our sins and was resurrected. But some would argue even these core tenets are questionable. It was not that long ago that a third of Anglican clergy were reported to not believe in the resurrection. When you get on to more fringe beliefs the questions are even more subjective. Do you have to believe the Bible is the word of God to be a Christian? Many would say so, but in what sense do you have to believe it? Do you have to believe in the virgin birth to be a Christian? Does Catholics' veneration of Mary make Protestant and Catholic irreconcilably different religions?

If you define Christianity by certain beliefs it is clear there will be many different interpretations of what it means to be a Christian.

But the second option is hardly less subjective. The other approach is to say it is not for others to define who is in and who is out. If you self-identify as Christian then fair enough, you are a Christian. This is similar to the view of a state religion such as the Church of England where the basic principle is everyone is in unless they say they are out. By contrast a more sect-like approach would be to say everyone is out unless they say they are in.

On one level the question fundamentally does not matter. If someone claims to adhere to a religion, that religion has a level of responsibility for them. ISIS claims to be Islamic. Therefore Muslims have a responsibility to denounce or refute it.

Similarly with Kim Davis, on a public level it is irrelevant that she does not believe in the Trinity. She professes Christianity and therefore Christians have a responsibility to respond. The same principle applies for the LRA and the KKK.

But here is the crux. Christians expect to be listened to when they deny that the LRA or the KKK reflect Christ's intentions. So in the same way we must be prepared to listen to Muslims when they deny that ISIS reflects the Qur'an's intentions. Of course Christians can debate how close ISIS' behaviour is to how Muhammad's in a similar way to how they should expect questions on whether the LRA reflect biblical principles. But if Christians expect to be listened to in their defence they must also listen to Islam's defence.

All religions have distasteful people and groups who operate in their name. We should give each the room to defend the true principles of their belief against unwanted perversions.

Follow Harry Farley on Twitter @HarryFarls.