Marriage with a woman who is atheist...

Marriage with a woman who is atheist, or blasphemer, or apostate, or a woman who declares animosity against Ahlul-Bayt, or the extremist (one who believes Ali is God) is not allowed; and the same applies to man with the addition that marriage of Muslim woman with a non-Muslim man is not allowed either. It is undesirable/discouraged (Makrooh) that one temporarily marries the fornicatress who is not famous for practicing fornication. Conservative way is to avoid marrying her at all.

As for the woman who is famous for committing fornication like a prostitute, it is forbidden to do Mut'a with her, unless she repents. Her repentance is known if she was called to commit sin and she refused; then that should indicate her trustworthiness, and an indication for the possibility that she may revive her soul with the opportunity of temporary marriage and being in the company of a person who can guide her to the right path.

Nonetheless, it is highly encouraged that the wife in both temporary and permanent marriage to be modest and temperate, not reckless or cheap. It is recommended that a Muslim man contract a temporary marriage only with a chaste ('Afifa) Muslim woman. Here chaste means someone who has never committed fornication and who follows the Shari'ah in her activities, and in general is honest and upright.

The two attributes 'Muslim' and 'chaste' are mentioned in the following two tradition: Imam al-Ridha (AS) was asked: "Is it possible for a man to contract a temporary marriage with a Jew or a Christian?" He (AS) answered: "I would prefer that he engage in Mut'a with a free Muslim woman." (Wasa'il al-Shia, v14, p452). To a question about performing Mut'a, the Imam Ja'far replied: "It is permissible. So marry none but a chaste woman, for God says, 'And those who guard their private parts' (23:5).

Hence you should not put your private parts where you do not feel safe with your dirhams." (Wasa'il al-Shia, v14, p452). How to distinguish a modest and temperate woman? In the case that one may have suspicious to the unknown woman who want to offer the temporary marriage, one way is to test her, yet this is not necessary as we will discuss shortly. It was reported that a modest woman was astonished when a believer asked her to commit the sin of fornication.

She thought the man committed sin by saying such thing. She did not know that it was a test with no lying meant. That was a question and not a decision to do wrong.