Is it permissible for the one offering the sacrifice (Al-Udhiyah) to give his share of the sacrifice to a charitable organization for distribution, and is it permissible to distribute the entire sacrifice without taking any from it or giving any as a gift, knowing that giving the share to the organization was not in fulfillment of a vow?

It is permissible to share in the sacrificial animal (Udhiyah (definition)), and it is obligatory to give in charity what is considered meat. It is more virtuous to give most of it in charity, based on the Almighty's saying: "So eat thereof and feed the distressed and the poor." As for eating from it, it is recommended according to the majority of scholars, and the Dhaahiris made it obligatory. Eating from it is more prudent. There is no harm in giving the entire Udhiyah in charity, though it is preferable to eat from it, and many scholars recommended dividing it into three portions. There is no harm in not giving your share of the Udhiyah to the association, as long as you have not uttered a vow.