I would argue that soccer has reflected change in societies more than actually effecting much change. But certainly events on the pitch (or in the stands) have contributed to change, or at least have shed light on broader issues within society. I will list and discuss a few examples below.
In 1990, a riot broke out at a match between fierce Yugoslavian rivals Dinamo Zagreb (in Croatia) and Red Star Belgrade (in Serbia.) Fighting in the stands spilled over onto the pitch, and Serbian police and fans began attacking Zagreb supporters and even players. One Zagreb player, Zvonimir Boban, attacked and kicked a police officer who was beating one of the club's fans. The incident was and is seen as a major flashpoint in relations within Yugoslavia, and a defining moment in Croatian nationalism.
Another example of football's ability to effect change is the triumph of the French national team in the 1998 World Cup. The team, which included several players descended from French colonial peoples, was seen as a symbol of a new, diverse France. The debate over multiculturalism in France has continued though, as several national federation officials were recently recorded bemoaning the number of African players in the national team system. Many others have pointed to the German national team, which now includes several players of Turkish descent, along similar lines.
The bottom line is that football clubs in many countries are so deeply embedded in the local culture that any scandal involving the game is bound to have social and cultural ramifications. Whether corruption in Italy, drug money used to finance Colombian clubs in the 1990s, Spanish clubs like Barcelona (Catalan) and Athletico Bilbao (Basque) that are associated with nationalist movements, football has often been at the center of major political debates and social change.