Generally speaking, if a religion does not identify as a denomination of Christianity, the simple response to a Bible quote is "I don't care". You can quote the Bible at a Hindu, a Buddhist, a Sikh, an Evolutionist, a Scientologist, a Satanist or a follower of various other religions and they won't bat an eye. Even many Jews are selective in the scriptures they will accept. Only a minority of Jews believe the New Testament, and some Jews accept only the Torah.
But Muslims have a problem in that they can't simply dismiss the Bible. In numerous places in both the Qur'an (Qur'an 3:55; 3:71; 5:47; 5:50; 5:71; 10:94; 29:46; 42:13; 61:14) and the Haddith (e.g. Sunan Abu Dawud Book 38, Number 4434), Islam speaks very highly of Judeo Christianity, and especially of our scriptures. The Torah and the Gospels are especially affirmed as inspired books revealed by none other than Allah. This leaves Muslims with an unusual dilemma. They must affirm scriptures that disagree with their religion. In other words, if the Bible is true, Islam is false because it disagrees with the Bible. If the Bible is false, Islam is false also, because it affirms a false book. In both scenarios, Islam is false.
In order to get around this dilemma, Muslims claim the Bible has been corrupted in various ways. They still acknowledge that it has some truth in it, especially when they try to show that the Bible disagrees with the Trinity, or when they think they've found Muhammad's name, but conveniently discount anything in the Bible that contradicts Islam as a corruption.
But rather than using Islam as the standard by which the Bible should be judged, the Bible should be used to judge the Qur'an. Partly because the Qur'an says to do this anyway (Qur'an 5:47; 5:50), and thus the Qur'an is utterly useless if Muslims don't judge by the Torah and the Gospel, but also because the Bible was complete (Revelation was finished in 95 A.D.) a full 470 years before Muhammad was even born (in 571 A.D.).
For Muslims to claim the Bible has been changed because it disagrees with Islam is illogical on a number of levels. It is illogical because it is circular, assuming Islam is true and using that as a counter to anti-Islamic arguments. It is illogical because the Bible came first, and we have manuscripts older than Islam to prove that the Bible we have today is the same as the Bible Muhammad had. It is illogical because both Islam and Christianity affirm that the word of God cannot be changed. The fact that the Bible contradicts Islam, rather than proving the Bible has been changed, proves that Islam simply cannot be true.