What is the ruling on a woman leaving her home without covering her head and hair, and is she an unbeliever (kafirah), a polytheist (mushrikah), or a disobedient one ('asiyah)?

A woman going out with her head uncovered or any part of her 'awrah (intimate parts) exposed in front of non-mahram men is a grave sin, but it is not shirk (associating partners with Allah) or kufr (disbelief). This act is haram (forbidden), and the evidence for its prohibition is the statement of Allah the Almighty: "And do not display yourselves as [was] the display of the former times of ignorance," (Al-Ahzab 33:33) and the saying of the Prophet, peace and blessings be upon him: "Two types of people from the inhabitants of Hell I have not seen... And women who are clothed yet naked, inclining [to evil] and themselves inclined [to evil]. Their heads are like the humps of leaning camels. They will not enter Paradise, nor will they smell its fragrance."