The "Boikot Jacaranda FM" Facebook group said its members "do not want to live in the past" and want to expose the "double standards in this country regarding voicing racial issues".
Organiser of the group, Mariaan Knox, said starting the Facebook page was the "only way for us [Boikot Jacaranda] to successfully voice our grievances".
Knox is the organiser of the first boycott group, which led to another Facebook page that has to date attracted about 29,000 people.
"I think I talk not only for myself, but for the majority of South Africans –- there [are] double standards in this country regarding voicing racial issues," she said.
Knox made reference to two TV and radio presenters, whom she would not name, both white males, who were "immediately fired" because of racial issues in the past.
"They did not even have a chance to voice their opinion regarding the incident," she said.
"Majority of the black population believe that all white people and especially Afrikaans speaking white people favour or applaud racism and apartheid, which is most certainly not the case."
Knox believes Morake misused her platform on Jacaranda FM's breakfast show.
"I feel that a radio station is a place where you need to have an unbiased opinion, a space for entertainment... [it is ] not a stage to voice your own political opinion and forcing all the listeners [at] that specific time to listen...," according to Knox.
"The majority of the black population believes that all white people and especially Afrikaans-speaking white people favour or applaud racism and apartheid, which is most certainly not the case," she said.
Morake, who joined the station three months ago, was reflecting about South Africa's democracy and said that there was little retribution for black people.
"It's like a child whose bicycle was taken forcefully away from him and then you say to the bully, 'no, no, no, share the bike together, don't be like that,'" Morake said
Some of the station's listeners said this was a racist remark, saying that Morake was calling white people bullies.
"We are not bullies, we are not racists... now all the people [who] feel the same can see and read that we as whites are now fed-up," Knox said.
She said Morake should not be given any form of special treatment for her utterances.
"I demand that all people should abide [by] the same set of rules, leave politics to the news. I demand a public apology from Tumi, [in] public, not [from] management."
Jacaranda FM management is still -- a week on -- not commenting on the matter, neither is Morake.