Praise be to Allah.
Meat slaughtered by one who is junub or menstruating is halaal, and there is no sin on him for that.
Ibn Qudaamah (may Allaah have mercy on him) said: If he is junub, it is permissible for him to say Bismillaah and slaughter (meat).
That is because the one who is junub is allowed to say Bismillaah (in the name of Allaah) and there is no reason why he should not do that. It is only forbidden for him to read Qur’aan, unless he recites from memory. Hence it is prescribed for him to say Bismillaah when he starts to do ghusl. Janaabah is no worse than kufr, and kaafirs may say the name of God and slaughter meat.
Among those who state that meat slaughtered by one who is junub is allowed are: al-Hasan, al-Hakam, al-Layth, al-Shaafa’i, Ishaaq, Abu Thawr and ashaab al-ra’y. Ibn al-Mundhir said: I do not know of anyone who did not allow that. And it is permissible for a menstruating women to slaughter meat, because she comes under the same rulings as one who is junub. End quote from al-Mughni, 11/61
Al-Nawawi (may Allaah have mercy on him) said in al-Majmoo’ (9/74): Ibn al-Mundhir narrated that there was scholarly consensus that meat slaughtered by one who is junub is permissible. He said: As the Qur'aan indicates that meat slaughtered by people of the Book is halaal even though they are naajis, then it is more appropriate that meat slaughtered by one who the Sunnah has stated is not naajis should be permissible. And he said: A menstruating woman is like one who is junub. End quote.
The fuquaha’ quoted as evidence for that the report narrated by al-Bukhaari (5501) from Ka’b ibn Maalik, according to which a slave woman of theirs was tending sheep in Sal’, and she saw that one of her sheep was dying, so she broke a stone and slaughtered it, but he told his people: “Do not eat it until I go to the Prophet (peace and blessings of Allaah be upon him) and ask him, or until I send someone to him to ask him. He went to the Prophet (peace and blessings of Allaah be upon him), or sent someone to him, and the Prophet (peace and blessings of Allaah be upon him) told them to eat it.
Sal’ is a well-known mountain in Madeenah.
It says in Sharh al-Muntaha (3/417) This shows that it is permissible to eat meat slaughtered by a woman, a slave woman, a menstruating woman and one who is junub, because the Prophet (peace and blessings of Allaah be upon him) did not ask for any details about the woman. End quote.
And Allaah knows best.