Even the South African Zionist Federation is divided on the issue after its vice-president Joselle Reuben supported the petition initiated by David Hersh, who caused a stir when he said that Tutu "ventures where angels fear to tread, not because he is brave, but because he is ignorant."
Federation Chairman Avrom Krengel distanced his organisation from the petition, saying that Hersch had done this in his personal capacity.
Hersch started the petition in response to a call by Tutu late last year for the Cape Town Opera Company to withdraw from performances in Israel because Palestinians would not have equal access to the shows.
Hersch accused the Nobel Peace laureate of being "bigoted" trying to "hijack" the language of apartheid.
The petition read in part: "We, the undersigned, with deep regret, do respectfully demand the resignation or termination of Archbishop Emeritus Desmond Tutu as a patron of the Cape Town Holocaust Centre and the Johannesburg Holocaust and Genocide Centre."
"Archbishop Emeritus Tutu's most recent endeavours at coercing world academic institutions to cut ties with those in Israel, as well as his most recent attempt to stop the Cape Town Opera Company from performing in Israel, are only the most recent examples of Archbishop Tutu's anti-Israel behaviour."
With 397 signatories to that petition, a counter petition launched by "Group of Concerned People" in support of Tutu had already secured 2,486 signatures by this morning.
Former chief justice Arthur Chaskalson, human rights lawyer Joel Joffe and singer Annie Lennox are among the prominent people who have signed the counter-petition in support of Tutu, which was started by members of Open Shuhada Street, an activist organisation campaigning for rights in Israel and the Palestinian territories.
The counter petition said: "For his advocacy of non- violence and human rights, Archbishop Tutu is an ideal patron for the Holocaust Centre because he reminds us that we have the strength and the duty to struggle against racism and violations of human rights at home and in every country.
"To call him an anti-Semite, because he has attacked the policies of the Israeli government, is outrageous, renders the term meaningless and enfeebles the necessary efforts to defeat real anti-Semites and racists."
Tutu also found support from the Muslim Judicial Council."An attack against Desmond Tutu is an attack against the struggle against Apartheid as his legacy symbolises the strength of good men who led this nation towards the liberation of the people of South Africa," said Moulana Ihsaan Hendricks of the council.