Question

Anti-federalists opposed ratification of the constitution until they were assured that ?

Answer 1

Anti-federalists opposed ratification of the constitution until they were assured that it would not interfere with the natural rights of citizens, which is why they insisted on there being a "Bill of Rights" that explicitly protected these basic rights. 

Answer 2

Anti-Federalists opposed ratification of the Constitution until they were assured that individual rights would be guaranteed by a bill of rights.

The Articles of Confederation, in place prior to the ratification of the Constitution of the United States of America, had granted stronger authority to the states.  Patrick Henry and other Anti-Federalists were concerned about too much power winding up in the hands of the federal government and its executive branch, thus allowing a small number of national elites to control the affairs of the USA.  They feared this also would diminish the rights and freedoms of individual citizens.

The Bill of Rights, laid out in the first ten amendments to the Constitution, provided some reassurance to Anti-Federalists after the fight over ratification. The US Constitution was ratified in 1788.  The Bill of Rights was created in 1789 and ratified in 1791.