Its true in Calcutta as well. Worse, Muslim students from oustdie the city, do not get house rent in a Hindu house. Few got house by an assumed name, but had to vacate, once they were found offering Namaz inside their home.
So, there is nothing peculiar about Mumbai. Muslims never Mix with others. That's why this issue. The Sikhs do not have that taboo, and participate socially with Hindus.