The phrase that refers to colonists' approach to religion was: "Separation of church and state".
This phrase was important because it meant that there must be no law that establishes what kind of religion should people follow, they must be free regarding this matter. This phrase wanted to ensure man natural rights because religion cannot oppose to the social duties of each individual. Later this phrase was accepted as part of the effects of the First Amendment.
This was absolutely necessary due to the fact that the early immigrants who traveled to America had different religions, their main purpose was to assure no religious persecution of any sort, as well as to embrace their faith knowing that all religions are equal in the eyes of the law, with no special favoritism.