I can only speak to Christians living in the US, because that is what I am familiar with. I was raised Southern Baptist by a practicing father and left the faith at 12 years old. Many of my friends are practicing Christians, so rightly or wrongly, I feel that I understand many of their concerns. It is my intention to be fair and respectful to the Christian point-of-view. If I have made a factual error, please let me know.
I suspect that some American Christians when told that you are non-religious take that as a rebuke. Whether they are conscious of it or not, they probably carry the presumption that you were raised Christian, somehow found it lacking and rejected it. If true, this would be a rejection of something they hold most dear.
If you identified yourself as Christian that narrows the parameters, so they have some sense of who you are as a person. As different as a parishioner from a Pentecostal church is from one from the United Church of Christ, they know that they hold some beliefs and values in common.
Nonreligious is a category that is hard for them to pigeonhole. Does it mean you are an atheist, an agnostic, spiritual but not religious or something else?
The unknown can be a source of fear. One doesn’t know what to expect. For those Christians who believe that any religion besides Christianity is the work of the devil, a person who is spiritual but not religious will be seen as a well-meaning fool that has been tricked by satan into following an evil path.
The possibility that you may be an atheist is probably the worst in their eyes for a couple of reasons. Because an atheist doesn’t believe in God, they see it as a deliberate rejection of God, a form of arrogance.
Secondly the most public face of atheism is Richard Dawkins. Dawkins is antagonistic toward religion in general, but focuses most of attention on the Abrahamic religions. For some Christians, he is their only experience of atheism.
It seems to me that they would find the agnostic the most acceptable of the three. An agnostic is likely seen as someone who hasn’t had the courage to either accept (the Christian) God or atheism. The agnostic appears to be the most malleable and therefore easier to save.
For some Christians, the Bible is the ultimate reality. Everything starts from there. Everything else is what man created. Whereas for the secular person, ultimate reality is discerned by experience, reason and the tools of science. The very basis of reality of the two people are like night and day. To enter your mindset would be like pulling the rug out from under them.
Some Christians believe that morality only comes through God and may fear that you are an immoral person. As they get to know more nonreligious people, they may come to realize that morality is written into all our hearts (except for sociopaths).
©2017 Stephen L. Martin
Painting: Umberto Boccioni, 1913, Dynamism of a Cyclist