How can one reconcile two verses: one in Surah Luqman that urges companionship with parents even if they strive to make one associate partners with God, and another in Surah Al-Mujadilah that forbids showing affection to those who oppose God and His Messenger, even if they were fathers?

There is no contradiction between the two verses. The verse in Surah Al-Mujadilah prohibits befriending those who show enmity towards Allah and His Messenger, whereas the verse in Surah Luqman enjoins dutifulness and kindness towards parents, even if they are polytheists. This is because being kind to a disbeliever does not necessitate loving or befriending them. Allah Almighty says: "Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes - from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly." (Al-Mumtahanah: 8).