Is the father considered an apostate due to his slandering of religious matters and his associating with atheists, and does this negate the obligation of honoring one's parents towards him?

Shaykh Ibn Uthaymeen differentiates between an apostate disbeliever and a non-apostate disbeliever. The apostate must be boycotted if he is invited to Islam and refuses. The non-apostate disbeliever has rights of kinship. The حد الردة (prescribed punishment for apostasy) is not enforced in most places, so the apostate remains in need of da'wah (invitation to Islam) and نصیحة (advice), especially if he is a parent. This applies to someone who openly declares atheism. As for mere possibility or suspicion, he still retains the rights of Islam.