Is a women who does not wear hijab considered to be non-Muslim? Does it mean that Allah will not accept her good deeds, her prayers, her charity and her restraint from doing wrong? Can she hope to be rewarded for maintaining these Islamic values but be punished for not wearing hijab, as she will be for all her sins?
All acts of worship, prayer, fasting, giving charity, paying alms and so on, are accepted when they are done with the intention to gain closeness to Allah Almighty.
While ignoring hijab is a sin, it does not invalidate any other act of worship. A lady who does not wear hijab will be held accountable for that. This, however, does not affect her other responsibilities and rights.