* Egypt far more stable but tensions remain
* Islamists and rivals at odds over shape of new Egypt
* Calm swiftly restored after scuffles
CAIRO, Oct 12 (Reuters) - Tensions between rival Egyptian political factions erupted into scuffles on Friday during a protest against a court ruling that acquitted officials from Hosni Mubarak's era of ordering a camel charge against demonstrators in last year's uprising.
While the activists were united in anger at the court ruling, supporters and opponents of Islamist President Mohamed Mursi threw stones and bottles at each other, showing feelings still run high between rival groups trying to shape the new Egypt after decades of autocracy.
The charge by men on camels and horseback was one of the most violent incidents during the uprising that ousted Mubarak in February 2011. The case has been closely watched by those seeking justice for the hundreds killed in the revolt.
A court on Wednesday said it did not find evidence to convict the defendants in the case, including top Mubarak-era officials such as former lower house of parliament speaker Fathi Sorour and Safwat Sherif, a longtime Mubarak aide.
More than 2,000 demonstrators were in Cairo's Tahrir Square and a nearby street by Friday afternoon. Some demonstrators pulled down a scaffold podium that had been erected on one side of the square for speeches.
A new government is in place but Egypt does not have a new constitution or parliament. Islamists and liberals have been at loggerheads over the constitution, still at the drafting stage and which must be in place before a parliamentary vote is held.
"Down, down with rule by the guide," Mursi's opponents chanted in Tahrir on Friday - a reference to Mohamed Badie, the leader of the Muslim Brotherhood, the group Mursi officially resigned from upon taking office. Mursi's opponents say Badie still pulls the strings.
"Mursi, Mursi," the president's backers responded.
But protester numbers were far less than the throngs of people who have congregated in Tahrir at other times since last year's uprising that overthrew Mubarak after 30 years in power.
Demonstrators also gathered in Egypt's second city of Alexandria, where Mursi went to a mosque to perform Friday prayers before giving a speech there.
"We won't let anyone involved in corruption get away," he said, while urging protesters not to disrupt people's work. As he spoke, some chanted: "The people want the judiciary purged."
Political groups, including the Brotherhood, had called for a big turnout in Tahrir to condemn the ruling. Many Egyptians blamed the general prosecutor, perceived as a Mubarak loyalist, for not securing convictions.
In an apparent bid to appease the public, the president said late on Thursday he was moving Abdel Maguid Mahmoud out of that position to a new post, as ambassador to the Vatican, because Egyptian law prevents him being dismissed.
Mahmoud denounced the move and told Egyptian media he would stay on. The influential judges club condemned the decision, seeing it as a violation of judicial independence. Even some groups who wanted Mahmoud out, questioned the way it was done.
Mursi has won grudging respect from some opponents for pushing the army out of politics, after decades of rule by military men, and for raising Egypt's profile abroad.
But many Egyptians, with high expectations after the revolt, say he has not done enough at home, failing to deliver on his promises for his first 100 days like cleaning up cities and getting traffic moving in Egypt's congested streets.
(Reporting by Mohamed Abdellah in Cairo and Abdel Rahman Youssef in Alexandria; Writing by Edmund Blair; Editing by Pravin Char)