Is it permissible for a menstruating woman to enter mosques and to attend or give religious lessons?

It is impermissible for a woman in a state of menstruation to enter the women’s section of the mosque even if it is to attend lessons or memorize the Qur`an except if she is passing through due to the words of Allah Who says, O ye who believe! Approach not prayers in a state of intoxication, until ye can understand all that ye say,--nor in a state of ceremonial impurity except when you are passing by (through the mosque). [Al-Nisa`, 43]

A woman in a state of menstruation is in a more extreme state than a person in a state of major ritual impurity. This is because the latter can lift the state of major ritual impurity by bathing but a menstruating woman remains in a state of impurity until her period ends. It has been reported that the Prophet said, “I do not permit a woman in her menses or a person in a state of major ritual impurity to enter the mosque” [recorded by Abu Dawud, al-Baihaqi, and by al-Bukhari in Al-Tareekh Al-Kabeer]. Though the hadith is classified as weak, the majority of scholars put it into practice, it is cited in the fatawa of the early jurists, and is the opinion of the scholars of the four schools of jurisprudence.

Maliki scholars maintained the impermissibility of a menstruating woman entering the mosque even if she is merely passing through. This opinion is stated in Bidayat Al-Mujtahid by the Maliki scholars Ibn Rushd who said, “… Some scholars permit this i.e. a menstruating woman entering the mosque — whether she is passing through or stays inside it; these include Dawud al-Zahiri and his disciples.”
From the above, it is clear that the scholars who permit a woman in a state of menstruation to enter the mosque are the Zahirite scholars whose opinion is disregarded in favor of the opinion of the majority of scholars who include the scholars of the four schools of jurisprudence.
The concluded ruling

A menstruating woman may deliver or attend religious lessons if the place where the lessons are held is annexed to the mosque and not a part of it; it does not take the same ruling as a mosque. God the Almighty knows best.