Well for Christians its wrong in the sense when the bible says we should not be unequally yoked to an unbeliever. I could get into a big thing about it but a true genuine Christian shouldn't truly be unequally yoked with an unbeliever
Yes, someone of a Muslim background can marry someone of Christian background, of course. But if they are truly following their religion then no. Their lives would contradict, and they would have to spend their life believing that when their loved one died they were going to hell, never to be seen again.
It is allowed for a Muslim man to marry a Jewish or a Christian woman ~people of the scripture~ (if they were virgin )
Allah says :
( 5 ) This day [all] good foods have been made lawful, and the food of those who were given the Scripture is lawful for you and your food is lawful for them. And [lawful in marriage are] chaste women from among the believers and chaste women from among those who were given the Scripture before you, when you have given them their due compensation, desiring chastity, not unlawful sexual intercourse or taking [secret] lovers. And whoever denies the faith - his work has become worthless, and he, in the Hereafter, will be among the losers. Quran (5:5)
As long as you don't live in the Middle East area or Muslim populated areas. You could be killed or be threatened. It no, marrying someone with a different Religion is alright, it's just like marrying someone who is a different race than you. You just have to respect their beliefs.
Well, the Bible admonishes us: "Do not become unevenly yoked with unbelievers. For what fellowship do righteousness and lawlessness have? Or what sharing does light have with darkness?" (2 Corinthians 6:14) Would it not be hard to raise children based on two completely different set of values? That will be a stressful marriage.