The protesters allege that Mr Curnane sexually harasses the female teachers, disrespects the national anthem, condemns the Indian education system and is a racist.
A protesting teacher claimed: "He (Mr Curnane) doesn't like the Indian national anthem. He wants the music teacher to cut it short to 15 seconds."
While another alleged: "He calls the women teachers names like honey and sweetie. We are not comfortable (with such names). When one member did not reciprocate, her contract was terminated."
An agitated parent said, "Does he think we are still slaves. He doesn't want to recognise Mahatma Gandhi and Abdul Kalam. He even threw out a portrait of Abdul Kalam."
The school management denies all the allegations. They blame a few teachers, who were sacked by director Curnane for incompetence, for instigating the protests.
As the protests continued for a fourth straight day on Saturday and the school remained shut, many parents are now worried that their wards' education would take a hit.
Some students, who are preparing for public exams, even took the revision tests sitting on the floor outside the school gates.
Chandra Praksh, a parent, said: "My son is in class XII. I'm seriously worried." Another added that "Let the kids go to school".
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.