Will I be held accountable for refusing to marry a man who does not want his wife to work outside the home, given that I need to help my sick mother who requires my financial support, and given also that I refuse other men due to their lack of religiosity?

You have done well in your eagerness to marry a man of religious commitment and good character. The fundamental principle is that a Muslim should hasten to marry if it is made easy for them. If a man of religious commitment and good character proposes to a woman, she should accept him, as the Prophet, peace and blessings be upon him, said: "If someone whose religious commitment and character you approve comes to propose to you, then marry him. If you do not do so, there will be tribulation on earth and widespread corruption." There is no harm in rejecting a suitor if he does not permit lawful work, especially if there is a need for it. However, a solution should be sought with the brother.