Which is more meritorious: inviting non-Muslims to Islam or honoring one's parents, and is it presumed that non-Muslims will respond to the invitation?

Firstly, combine filial piety with da'wah (calling to Islam). Parents are not to be obeyed if they forbid calling disbelievers to Islam, unless harm would befall the da'i (caller) or them. Calling disbelievers to Islam is one of the most emphasized religious obligations for whoever is able. Disbelievers have responded to the call many times throughout history; many companions of the prophets embraced Islam, and many Islamic lands had polytheistic inhabitants who later believed.