According to Shia Muslim Scholars A Shi'ah Muslim man can marry: a Shi'ah Muslim woman and a non-Shi'ah Muslim woman. However, if there is danger of being misled, then it is haram.
He can also marry a Jewish or Christian woman in mut'a only. But he cannot marry a woman of any other faith.
A Shi'ah Muslim woman can marry: a Shi'ah Muslim man or a non-Shi'ah Muslim man, although it is better not to do so; and if there is danger of being misled, then it is haram. But she cannot marry a non-Muslim man.
About the reason, in fact we know few reasons of laws of Islam. Islam is a set of laws for human life provided by God and human is free to accept or reject them. In few cases the reason of some laws are mentioned in Quran or Hadith but mostly we do not know them. But there are many guess from scholars and scientists but they are not certain. I personally think this can be for preventing decrease in population of Muslims. Usually the religion of family is determined by father and mother is usually follower in father. I think is to have Muslim children instead of non-Muslim children and to spread Islam more.
Islamic Marriage (chapter 4, b. Restrictions based on Religion)
Why do Shi'as allow mut'ah marriage?
The fornicator does not marry except a [female] fornicator or polytheist, and none marries her except a fornicator or a polytheist, and that has been made unlawful to the believers.24:3