Did people try to fight back or protest against the Separate Amenities Act?

As with any radical government move, there was backlash and protest to the Separate Amenities Act of 1953. However, one central figure to the protests against Apartheid was Nelson Mandela. It is important to note, however, that racial discrimination was already advanced in South Africa before the Separate Amenities Act took place; "Whites Only" signs were prevalent many years before Apartheid began.
As the Afrikaner Party grew to existence in the 1940s, Mandela and his comrades began to lead peaceful protests such as strikes and boycotts of goods. Because organized labor was seen as a communist movement in South Africa, the majority power passed the Suppression of Communism Act of 1950. This law essentially stated that those participating in work stoppages, for whatever reason, could risk imprisonment. Because of this, most of the protests declined.
While Mandela favored peaceful protests and civil disobedience, violent action was becoming more common in the years following the Separate Amenities Act. The African National Congress Party eventually split into a group called the Pan Africanist Congress, which favored a more forceful approach. The PAC felt that violence was a necessary move in eliminating Apartheid, and this lead to sixty-nine protestors being massacred in the town of Sharpeville in 1961.
Mandela eventually served twenty-seven years in prison for his actions in the protests of Apartheid. However, upon his release in 1990 he embarked on a tour across Africa. Once again, he led peaceful opposition to Apartheid, and negotiations began to eliminate the discriminatory practices in South Africa. Apartheid was erased, and in 1994 Nelson Mandela was sworn in as president of South Africa.
https://www.history.com/topics/africa/nelson-mandela

https://www.latimes.com/archives/la-xpm-1990-06-20-mn-222-story.html