For the most part, it was decided muggles no longer needed to know and the solution was to alter memories. In reality, it was just a bunch of pretty words for obliviating people who had no way to protect themselves. While there may have been a few muggles who posed more of a risk with the knowledge; those few caused a panic. In the end only muggles with magical children not yet graduated or married to a magic wielder were allowed to keep the knowledge. These muggles were tracked relentlessly, to keep everyone "safe’.