Should HIV positive women be allowed to have children?

Yes. Yes. They have a right to have children like anyone else. As long as she sees a high risk OB and manages her HIV prenatally and during the immediate postpartum period, the risk for HIV transmission can be very very small.
They Are Allowed. Hiv-positive women can have children, and quite safely. There are medications and treatment plans that women can establish with their doctors to prevent transmission of the HIV virus to their babies.