Someone who is not willing to believe in Islam and is not willing to have anything to do with religious matters. How does Islam regard such a person?
If someone is told that there is a hell in the Hereafter and he says I don't care then he dies and sees "hey it is what I was warned about, alas, I wish I had not ignored it when I was alive so that now I could live in peace". What do you say about such a story?
You may say but I doubt if there will be a hell, then Islam asks how could you simply deny what you don't know be true or wrong? If you are sure that there is no hell in the Hereafter then you will have an excuse but I promise you no atheist exists that can claim such, they only say we don't believe in what has not been proved for us, God, religion, hell and etc., but then they will be asked if the reverse had been ever proved for them that they have easily accepted it!? Does anyone have a proof that there is no God, no religion and etc? NO! They just chose not to believe in such issues and they will be treated according to what they chose!
According to Islam, there are people who are not informed of even the probability that Islam might be the Truth (for this era), they will die and they are not guilty for what they didn't know, but the rest of people who have given information should research about it, anyone to the extent that he can, since the issue is so important and failure in this regard might cause eternal sorrow. That's all! Every man and woman should care why he or she are here living such lives, from where they have come and to where they will face and go toward. If someone searched with the good will and understood Islam is the Truth then he will find out that becoming a Muslim is just a beginning for preparing for a Journey for which this life is only a short Bonus level to start the evolution toward Perfectness. However, if someone tried but didn't reach the point to believe in Islam during his/her life then Allah will not ignore his/her effort in reaching the truth.
Also Islam claims that if someone starts with a pure will of finding the truth will not end his/her research anywhere but in accepting Islam.
So to answer your question in short, if someone is a person that knows nothing and has heard nothing about such religious concepts as God, the Judgment day, heaven and hell, then he will not be questioned about it, but after them almost all the persons (exceptions are always possible though) are responsible to search for the Truth and hesitating the issue is like hesitating to eat or not to eat a poisonous meal, the poison will do its work regardless of your decision, when the danger is big the caution is intellectually and thus religionally required.