Is someone who claims a permissible matter is unlawful, while knowing it is forbidden, or who mocks something from Islam, treated the same as an infidel who will abide eternally in Hell?

Declaring one's parents as disbelievers is a serious matter, and the duty is to treat them as Muslims, while striving to advise them with wisdom. A Muslim does not become a disbeliever merely by denying the unlawfulness of something forbidden, unless it is from what is known by necessity to be part of the religion. Mocking religion is disbelief, and it involves ridicule and contempt, but not everyone who commits an act of disbelief is necessarily a disbeliever.