Fundamental Rights
(1) All laws in force in the territory of India immediately before the commencement of this Constitution, in so far as they are inconsistent with the provisions of this Part, shall, to the extent of such inconsistency, be void. (2) The State shall not make any law which takes away or abridges the rights conferred by this Part and any law made in contravention of this clause shall, to the extent of the contravention, be void. (3) In this article, unless the context otherwise requires - (a) "law" includes any Ordinance, order, bye-law, rule, regulation, notification, custom or usage having in the territory of India the force of law; (b) "laws in force" includes laws passed or made by a Legislature or other competent authority in the territory of India before the commencement of this Constitution and not previously repealed, notwithstanding that any such law or any part thereof may not be then in operation either at all or in particular areas. (4) Nothing in this article shall apply to any amendment of this Constitution made under article 368.
This is the article that gives your Fundamental Rights real teeth. It says any old law that conflicts with your Fundamental Rights is automatically void (to the extent of the conflict), and Parliament or a state legislature cannot pass a new law that takes away or weakens those rights either - if they try, that law is void to that extent. This includes not just Acts of Parliament, but rules, regulations, and even customs that have the force of law. Clause (4) clarifies this doesn't stop Parliament from amending the Constitution itself through the proper amendment process.
If a state passed a rule requiring a religious test before someone could vote in local elections, that rule would violate the equality and non-discrimination rights elsewhere in Part III - Article 13 is what makes that rule void and unenforceable, giving you a real basis to challenge it in court.