The Vadakalai sect of Sri Vaishnavism says that women and shudras are not allowed to recite the Vishnusahasranama, but can only hear it. In fact, Iyers before the past 50 years also prohibited women and shudras from reciting it as well.
This is not as controversial as it seems because Shankaracharya in his Vishnu Sahasranama Bhashya has also said that shudras are not allowed to recite the Vishnushasranama, but they can only hear it. However, he doesn't make any mention of Dvija women.
Vadakalai Sri Vaishnava acharyas, and even Iyers before the past 50 years, prohibited women from chanting the Vishnu Sahasranama.
More information is found in this thread.
My question is, is there any scriptural rule that says they are prohibited from reciting it? I have tried to find out the scriptural reason, but so far it seems to be an Achara rule, that is presumably based on some scriptural rule that may or may not be forgotten.
But another complication is this: If they can hear it and read it, but not verbally recite it, does it mean that they can mentally recite it? Because if they can hear it, and if they hear it enough, they could mentally commit it to memory. So can they mentally recite it?