Is it permissible to give one's father a card to subscribe to Mesaieed Petrochemical Holding Company, given the difference of opinion among scholars regarding the permissibility of subscribing to it, and would that be considered participation in sin?

Since you do not wish to subscribe to the company due to the اختلاف العلماء (difference of opinion among scholars), this is a praiseworthy act of wara' (piety/caution). Your father should also be advised to be cautious. However, if your father insists and asks for the card to subscribe, fulfilling his request falls under obeying parents in matters of shubuhāt (dubious matters). Most scholars consider this obedience obligatory, because avoiding dubious matters is an act of wara', while pleasing parents is an imperative.