Qur'anic Verse

Qur'an 3:184: But if they reject you, so indeed were rejected before you messengers who came with clear arguments (al-bayyinat) and scriptures (al-zubur) and the illuminating book (al-kitab al-munir).

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Bayyinat is said to refer to the signs accompanying or miracles performed by the ancient prophets. It could also refer to their logical arguments.

"Scriptures and the illuminating book" is said to refer to the scriptures and/or religious laws and ordinances transmitted by the ancient prophets. For instance, Tafsir al-Mizan gives as examples the scriptures of Noah and Abraham, and the Torah and Injil. Some exegetes have specific views about which scriptures may be referred to by which phrase and others simply take it as an overarching phrase to refer to ancient scriptures. 

("Zubur" can refer to any scriptures not just the Psalms.)

This interpretation may be due to the fact that it is related that section of the Qur'an was revealed when some Jews came and questioned the Prophet. 

Maybe in the phrase "the illuminating book", there is a hint that all the revelation came from a single divine source, rather than the different scriptures being like books written by different people. 

It is not good to reduce this verse to a question of religious identity.

The verse is speaking about humans (and jinn) in general. Human beings have the potential to ascend above the level of the angels, or descend lower than the level of animals. 

One of the purposes of the human life is for the human being to develop their spiritual and human potential. People who do not use their God-given capabilities to think, reflect on, and draw lessons from the world around them (including to consider what is right and wrong and their reason for being), who focus only on consuming (like cattle), who blindly follow others (like sheep), or who care only about indulging in their animal desires fail to reach a minimum level of their God-given potential and, as a result, end up in Hell. This is especially true if their appetites and apathy leads them to harm others, take away the right of others, or blindly accept injustice.

So, basically, God created Hell for human failures. 

(Obviously this verse is not about people who genuinely are unable to contemplate some things, for instance, if they have a mental impairment.)

This is independent of whether a person identifies themself as a Muslim or not. Of course a true Muslim - not just a Muslim in name - would strive to rise above their animal side and would take heed of the Qur'anic injunction to think, reflect, and ponder on God, the creation, the human being, ethical matters, society, and how to live. 

In addition to what has been said, my understanding of this verse is with respect to the meaning of "wali/awliya" as putting one's self under someone else's authority. That is, one should not put one's self under the authority (in the sense of dependence or giving over power of one's self to someone else, e.g. politically, financially, personally) of someone who is not Muslim in such a way that one loses control over one's life or society and cannot easily recover it.

To my understanding, one of the principles of the early Muslim community was self-definition and self-sufficiency. It doesn't mean that one cannot be friends; friendship is different from disempowerment. To see the results of political or economic disempowerment, one can look at what happened during the colonialist era as an instructive example. (I am not saying that European colonialism was a morally Christian act, but just that this is how these dynamics can play out in the real world)

I would like to add that, in this day and age, no one would argue the reverse; that is, none of the Western countries (which are somehow connected to the Christian heritage even if they are not necessarily "Christian") woud put themselves under the political, legal, financial, or cultural authority of Muslims, yet no one says that this is prejudiced.