Is it permissible to declare a Muslim who differs with us in opinion or in worldly matters to be an infidel, and is this supported by the fact that Islam allowed the People of the Book to practice their rituals despite their rejection of the principle of monotheism?

The People of the Book are not permitted to disparage the religion of Muslims. Whoever disparages the religion, whether from the People of the Book or Muslims, shall be executed. As for deeming a Muslim an unbeliever merely due to a difference of opinion or fighting, this is not valid, because Allah Almighty says: {And if two factions among the believers fight, then make settlement between them} [Al-Hujurat: 9].