How can one reconcile the Almighty's saying: {That you may warn a people whose fathers were not warned, so they may be reminded} with the claim mentioned in some answers that the message of Abraham (peace be upon him) reached the parents of the Prophet (peace be upon him)?

The texts of revelation do not contradict each other; if they appear to contradict, it is obligatory to reconcile them. Accordingly, the two hadiths "My father and your father are in the Hellfire" do not contradict the verse "And We would not punish until We send a messenger," for two reasons: First, the people of the fatrah (interval between prophets) will be tested on the Day of Resurrection, and the Prophet, peace and blessings be upon him, knew that his parents would not respond, so they were among those who would not respond. Second, they are in the Hellfire due to the possibility that the call of a prophet reached them, such as the call of Ishmael, or due to remnants of the calls of previous prophets, and that the verses about not sending a warner did not mean that the call did not reach them. Punishment does not occur until the حجت (proof) is established by the messengers.