No, you should simply treat her as a neighbour and new American. It might be different if your father had directly confronted her, but there is no need to tell her about the sectarian hatreds she is already aware of.
In 1956 my father made me watch the newscasts when the marchers in Selma were brutally attacked by the police and their Klan supporters. He explained about racism and its evils, and told us not to fall for its advocates. Today I tell my grandchildren the same thing about sectarian violence.
Islam is a repressive religion. So is Christianity and, sadly, so is the Judaism of my family when followed literally. It doesn't matter which religion is pushing suppression of women, homophobia and violence against others, it remains wrong.
As for your father, you have not said how old you are so I cannot advise you on an appropriate response. While you live under his patronage you should respect his authority at least enough not to challenge his ignorance directly. That isn't for him. Your mother doesn't need the stress.