Is a son burdened by the sinful actions of his mother and sister that contravene Islamic law, and is he still obligated towards them after they cut ties with him because he forbade their wrongdoing?

Your mother consulting sorcerers is a grave sin, but it is not considered shirk (polytheism) that expels her from Islam. The greatest act of devotion to your mother is to strive for her rectification through supplication, seeking assistance from virtuous people who can advise her, and continuously advising your mother and sister regarding her going out with a non-mahram man before the marriage contract. Being patient with their boycotting you because of your advice, and being keen on maintaining ties with them even if they cut you off, holds great virtue.