How can the two hadiths be reconciled, those that address the rejection of a Muslim's offer and entering Paradise or Hell, and the cutting off of kinship ties and entering Paradise?

The Hadiths of warning (of entering Hellfire) and promise (of entering Paradise) indicate that deeds are a cause for punishment or reward. However, the fulfillment of this warning or promise depends on the presence of conditions and the absence of impediments. Among the impediments to the warning taking effect are: repentance, seeking forgiveness, expiating good deeds, worldly afflictions, the intercession of intercessors, and Allah's mercy. As for the warning or promise, it does not necessarily apply to everyone who commits the act, as the ruling may be averted due to the presence of an impediment, such as Allah bestowing His mercy upon the person, or the intercession of intercessors, or expiating repentance, or outweighing good deeds.