Naidoo said this was not a matter of denying the Chief Justice his rights as a citizen but the office he holds requires that he respects the Constitution.
"This is his primary responsibility, one that comes with holding high public office.
"If the Chief Justice wishes to comment on issues extraneous to his position as the head of the judiciary, he will be free to do so when is no longer constrained by the responsibilities of that office."
Mogoeng also received backlash from several other bodies, with one even considering laying a complaint with the Judicial Service Commission (JSC).
On Friday, the EFF called on Mogoeng to withdraw his comments and to "join all progressive voices in an unequivocal condemnation of apartheid Israel".
"He must realise that Palestine needs people of the world to unite behind them as they fight for self-determination; this is just the thing to do," the party said.
ANC national spokesperson Pule Mabe said Mogoeng had entered the arena of political commentary, which might make him vulnerable should he adjudicate a human rights matter in future.
Consulting legal advisors
Mabe said: "It was rather unfortunate for the Chief Justice to state that the 'South African government policy was binding upon himself and that he was not seeking to reject it', but then clearly and openly opposes it as a citizen."
Human rights organisation Africa4Palestine said it was in the process of consulting with its legal advisors over Mogoeng's criticism of South Africa's foreign policy.
Africa4Palestine is to lay a complaint with the JSC against Mogoeng.
"It is regrettable that the Chief Justice has publicly entered the Israeli-Palestinian issue on the side of the oppressors - the Israeli regime," spokesperson Tisetso Magama said in a statement last week.