What is the ruling on consuming food and wealth, and accepting gifts, provided by my sister and her husband who work in a judiciary based on man-made law? And does that affect the acceptance of prayers?

The majority of scholars are of the opinion that it is impermissible for a woman to hold the position of a judge, whereas Abu Hanifa permitted her to judge in financial matters but not in cases of Qisas (retaliation) and Hudud (prescribed punishments). Muhammad ibn al-Hasan and Ibn Jarir al-Tabari permitted a woman to be a judge in all cases. However, Ibn al-Arabi denied the authenticity of this view attributed to Ibn Jarir al-Tabari, and he interpreted Abu Hanifa’s statement to mean that a woman may judge in matters where her testimony is accepted. If the profession of your sister and her husband is unlawful, then the salaries they receive from it are considered illicit wealth (haram money). Illicit wealth is a reason for prayers not being answered. Therefore, try to distance yourself from any money they bring, and do not cease advising them to avoid that job and to repent to Allah.