* Egyptians celebrate Eid
* Political sides stage separate rallies in capital
* Tension underlies festivities
By Maggie Fick and Shaimaa Fayed
CAIRO, Aug 8 (Reuters) - Bitterly divided Egyptians prayed in public and children played as they celebrated the Eid al-Fitr holiday on Thursday.
But the barbed wire and armoured vehicles in the streets of downtown Cairo and the barricades around Islamist protest camps attested to the dangerous political edge to the festivities.
Rival supporters of ousted Egyptian President Mohamed Mursi and the new army-installed government converged on separate sites in the capital of the Arab world's most populous nation against the background of crisis.
Families flocked to dawn prayers at the Rabaa al-Adawiya mosque, focal point of Islamist opposition to the government, then strolled and picnicked around the area.
"This is the best Eid of my life," said Ali Mohamed, 40, a farmer from a village near the Nile Valley town of Minya, south of the capital. "It's victory or death now. We had five elections and that traitor Sisi has reversed all that."
He was referring to army chief General Abdel Fattah al-Sisi, who led the overthrow of the Islamist Mursi on July 3 after huge demonstrations against his rule.
Egypt has been dangerously polarised since then with Mursi's Muslim Brotherhood and its loyalists demanding his reinstatement and the government and its supporters saying they are finished.
Tension has prevailed at the Brotherhood protest camps after the security forces threatened to dismantle them. Protesters have erected sandbag-and-brick barricades and armed themselves with sticks to confront any attack.
But Eid - the four-day holiday which marks the end of the Muslim fasting month of Ramadan - offered a measure of relief.
Thousands packed into the Rabaa camp, spilling onto a street where security forces shot dead more than 80 Mursi supporters in clashes on July 27.
Boys lit firecrackers and worshippers handed out sweets and offered greetings to each other, an Eid tradition. Street stalls sold tea, snacks and plastic toys.
Others hawked posters of Mursi and green headbands with the Islamic inscription "No God but God". One table sold tear gas masks and swimming goggles.
Groups chanted "Interior ministry thugs! "Egypt, our country," and beat drums.
"We want to live as free Muslims," said a 45-year-old English teacher, who gave her name only as Emmy. She wore a full face veil and gloves, a style favoured by the ultraconservative Salafi Muslims.
"We don't want to be insulted in police stations. We don't want to be harassed for wearing these veils or for growing beards."
She said she wanted to work as an interpreter but companies would not hire her because of her dress.
Emad Abdelaziz, 53, an engineer, attended prayers with his wife and three daughters, all dressed smartly for the occasion.
"We came to Rabaa for the prayer because this year is not like any other. We are here to demand Mursi's return," he said.
Ghada Idriss, 35, had travelled from rural Minya province with her husband, two young sons, and two-month-old daughter.
"I came here because I want to make a small difference," she said. "By sitting here peacefully, they will understand and know that we refuse the return of the system of Hosni Mubarak."
Supporters of the government began gathering in Tahrir Square, the focal point of the uprising that brought down long-ruling strongman Mubarak in February 2011 and set in train Egypt's prolonged and troubled revolution.
Some leftist and youth groups called for public prayers in the square to support what they regard as the second revolution -- the overthrow of Mursi with mass public demonstrations.
Soldiers lounged atop armoured personnel carriers in the streets off the square, including outside the Egyptian Museum, home to a trove of antiquities for the age of the pharaohs.
Awad Abdel Gawad, a 60-year-old woodworker, said: "I am here to say happy Eid to the people of the revolution, of Tahrir Square. I want the revolution's demands met and the country to flourish. Every revolution has troubles at the start but God will help us."
Mursi supporters at the Rabaa and Nahda protest camps should avoid violence and give up peacefully, he said.
"The Rabaa people think Mursi's coming back but he isn't. He is gone," Abdel Gawad said.
"I want to tell those in Rabaa 'we are all Egyptians, all Muslims, and what harms you harms us, and we want a president who fixes the country and we are all with him."
Although Mursi was democratically elected in June 2012, his rule divided the country. Many Egyptians feared he was trying to impose an Islamist regime on the country of 84 million people, while he failed to get to grips with a deteriorating economy.
The army justified his overthrow by saying it acted at the behest of millions who took to the streets to demand that he go.
Reem Adel, 17, a student at the University of Commerce, said she was at Tahrir to celebrate Eid prayers and commemorate the people she said had died under Mursi's rule. She gave a cautious endorsement to Egypt's new military strongman.
"Sisi has been good so far though we are worried about the future. We want Rabaa and Nahda dispersed but with the least loss of life because we are afraid violence would be used against us too later," she said.
On a stage in the centre of the sprawling Tahrir Square, a singer sang anti-Brotherhood rap and nationalist songs. Hundreds of mostly young people came early to the square, which was expected to fill up later in the day.
Portraits of Sisi hung from trees and lamp-posts, and some banners denounced U.S. President Barack Obama and U.S. Ambassador Anne Patterson - perceived by government supporters as favouring the Islamists.
Flag vendors sold banners saying: "Egypt is guarded by the army. The Egyptian people delegate the Egyptian army to fight terrorism." (Reporting by Maggie Fick and Shaimaa Fayed; Writing by Angus MacSwan; Editing by Paul Taylor)