Shaykh al-Islām was asked:

For which acts are the two forms of purification—ritual bathing and ablution—obligatory?

He replied:

They are obligatory for prayer, whether obligatory or voluntary, according to the Quran, the Sunnah, and scholarly consensus. There is disagreement concerning circumambulation and touching a copy of the Quran. There is also disagreement concerning the prostration of recitation and the funeral prayer: do they fall within the meaning of prayer for which purification is obligatory?

As for devotional retreat in the mosque, I know of no one who has said that ablution is obligatory for it. The same applies to remembrance of Allah and supplication, for the Prophet, peace and blessings be upon him, instructed menstruating women to engage in these. As for reciting the Quran, there is an isolated dissenting view.

The position of the four imams is that both forms of purification are obligatory for all of this, except that disagreement has been reported concerning circumambulation in a state of minor ritual impurity. The four imams likewise do not permit a person in a state of major ritual impurity to recite the Quran or remain in the mosque if he has not performed ablution. They differed concerning recitation by a menstruating woman and recitation of a small amount. There is disagreement on this within the school of