Sameh Ashour, the head of the lawyer's syndicate, was one that withdrew days before the court order.
Mr Ashour said the NSF would not contest the polls under an election law which critics said favours Islamists.
Some members of the Supreme Council of Armed Forces may also back him "because he might maintain the status quo, " Ashour said.
His supporters include "the powerful ones, a collection of businessmen and generals, " said Ashour, a visiting scholar at the Brookings Institution in Doha, Qatar.
There could still be an appeal against the administrative court's ruling, although the Freedom and Justice Party has said it accepts the decision, Ashour said.
CNN: Row over Egypt's new constitution reflects wider tensions
But Matthew believes their biggest threat will come from Egypt, who are ranked second for the tournament and led by world number two Ramy Ashour.
Matthew's victory will return him to the top of the world rankings above Egypt's Ramy Ashour, who made a second-round exit in Al Khobar with a damaged hamstring.
Other key appointments include Abdurrahim Bin Yazza - a former executive with the Italian oil giant ENI - as head of the oil and gas ministry and Ashour Bin Khayal, as interim foreign minister.
"This is the first time in Egypt's political history that an elected civilian politician overrules the decisions of the heads of the military establishment, " said Omar Ashour, a visiting scholar at the Brookings Institution's Doha Center.
Once the panel is reconstituted, its members will not be starting from scratch in drawing up a draft, since Egypt has had three previous constitutions and various political and civic society groups have drawn up models, Ashour said.
CNN: Row over Egypt's new constitution reflects wider tensions
"Parliament will discuss tomorrow the new process of choosing the 100-Egyptians who will write the country's most important guide to governance so they must be careful in their choices and it must include constitutional lawyers and experts this time around, " Ashour told CNN.
Ashour believes the recently announced candidacy of Omar Suleiman, Egypt's former vice president and head of Egyptian intelligence, may galvanize the nation's revolutionary and Islamist factions to work together to prevent a return to power of the man who is seen as the essence of the old regime.
CNN: Row over Egypt's new constitution reflects wider tensions
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