After the war, all the world leaders came together to discuss a way to prevent anything like AFO and the League of Villains from ever happening again. Months later the Quirk Accords were written — a worldwide ban on quirks for all except trained Pro-Heroes — and the Super-Enhanced Human Registration Act that required all individuals quirks to be tracked and heroes to register their quirks in a national database. Countries were left to uphold laws in their own ways. Researchers around the globe devised methods to remove quirks but Japan devised a procedure that would extract quirks from a person's DNA with the help of a drug derived from Kai Chisaki's prototype. When the laws went into effect heroes had two choices: Continue as heroes, protecting the city from criminals and bringing in those who refuse to give up their quirks. Or relinquish their quirk and retire early.
Fifty years later, the time of the canon cast is now over. Most of the public has settled back into a lull of normal, comforted by the fact that heroes will protect them from errant quirks, law breakers, criminals, and villains. The law didn't stop people from trying to hide their quirks but they were the minority, the public happy with the sense of safety. Such actions put them immediately on law enforcement and hero radars, hunted down night and day relentlessly much like Villains. Capture, forced quirk removal, monetary fines, and jail time are the penalty for evading the quirk ban without exception.
The quirk removal process did not completely remove the quirk factor within their DNA but it did remove all superpowers and abilities. For Heteromorphic-types, otherwise known as Mutants, this did not remove their extra features. This made them targets for discrimination, harassment from law enforcement, and often refusal of service in various establishments.
The Resistance rose up in the shadows; a collection of smaller groups operating independently. Every group has it's own goal, leader, morals, and methods to oppose the government. Some take in individuals, children, and families to protect their quirks. Others fight openly with heroes and the government, choosing a more terroristic method. Some choose a more peaceful route with protests and petitions. Others try a political journey, aiming to change the laws from within.