The protesters camped outside east Cairo's Rabaa al-Adawiya mosque have lived with the fear of violent dispersal for more than a fortnight, but that did not stop housewife Aza Galal pitching camp there with her six-year-old son last Thursday.

"We don't care about death," said Galal on Monday afternoon, her hijab resting underneath a rainbow-coloured parasol, her son Saif tugging at her clothes. "We believe in one thing. When your time to die comes, you will die. So will you die as a courageous martyr, or as a coward? That's the point: we want to die as martyrs."

Since the end of June, tens of thousands of supporters of the deposed Egyptian president Mohamed Morsi have camped on two sites in Egypt's capital, one near the city's university, west of the Nile, and the other across town at Rabaa. At first, the protesters were mostly from Morsi's Muslim Brotherhood, and they gathered to demand his rule continued; once Morsi was overthrown by the army on 3 July, after days of mass protests, they then pushed for his reinstatement.

As the weeks passed without Morsi's release from detention, this demand has seemed increasingly unlikely to be realised – and the protesters increasingly in danger. State officials have promised to forcibly disperse the camps for a fortnight, prompting fears of a third state-tolerated mass killing of Morsi supporters in a month. Fears grew on Sunday, as rumours swirled that the crackdown would happen at dawn on Monday, but the camp was untouched.

Despite the constant threat of an attack, the camps have become increasingly organised and entrenched – becoming more like tent cities.

The camp at Rabaa, on a blocked-off suburban crossroads, sits behind several makeshift walls – some built with cement, others with sandbags and still more with paving stones ripped from the street. Street vendors sell water pistols, sunglasses, groceries and fruit. One tent houses an exhibition about those killed during protests earlier in the month. At the centre of the crossroads, preachers speak from a large stage, or lead prayers. At the southern entrance, a large marquee built for last week's Eid celebrations contains a mini fairground.

Despite the real threat of further bloodshed, the protesters are going nowhere. "When I heard that the sit-in might be attacked on Monday, I came back running" said Moaz Ahmed, a teacher who helps to police the four entrances to the camp, where there are bag and ID checks. "I don't care if I die or not."

Ahmed was unarmed, with only a blue crash-helmet and a Manchester United tracksuit for protection. But Cairo residents and human rights activists say there may be more deadly weaponry inside. Several bodies bearing marks of torture have allegedly been found in the region of the camp, prompting allegations that it houses torture cells. Those at the camp claim that the only people hurt at Rabaa are thieves and infiltrators from state security. "If there's a thief, he will get a fair beating," said Gehad al-Haddad, a Brotherhood spokesman. "But we will take him outside the sit-in [afterwards] and we will let him go."

Critics of the campers argue they simply seek martyrdom instead of solutions, and that they pander to naive western sensibilities. But campers claim they have real grievances and face worse bloodshed if they return home without the new military-backed government guaranteeing their safety. And for most, after the massacres of recent weeks, the only guarantee that would mean anything would be the return of Morsi.

"If we leave the square, it will be worse than the 90s," said Suzanne Abdel Qadir, referring to the brutal Hosni Mubarak-era crackdown against the Islamists. "We're back to the days of oppression under Mubarak. If we go home then the fight is over." Morsi's critics point out that while Islamists had an easier time during his presidency, he never attempted to tackle wider police brutality.

"I'm prepared to be here forever, until our president comes back," said Aza Galal. "We all voted for democracy. And then because some people gathered in Tahrir Square, they put our votes in the rubbish bins."

Opponents of Morsi argue that while he was elected democratically, he was uninterested in upholding wider democratic values and only served the interests of the Muslim Brotherhood. In an attempt to counter this argument, Rabaa's organisers have erected large English-language signs that suggest the camp houses a broad spectrum of beliefs. "Artists for Morsi" hangs over one tent. "Liberals for Morsi" stands next to another empty tent. The most speculative, "Christians for Morsi", stands with "Christians" crossed out. Elsewhere in Egypt, attacks on Christians have risen since Morsi's removal – incited, some allege, by Islamist extremists.

The makeup of the camps is varied, but not in the way that their organisers suggest. While the camps were begun by the Brotherhood, who remain the largest faction, the Brotherhood no longer completely controls settlements that also contain ultraorthodox Salafi factions from hardline groups such as Gama'a Islamiya – or those unaffiliated with any Islamist group, such as Aza Galal, who travelled with her husband from Alexandria.

These divisions cause tensions. The young, western-oriented Brothers who organise the speakers' rota at the central stage complain of Salafis seizing the microphone uninvited. The Guardian was asked by a senior Brotherhood official to stop interviewing a Salafi for fear that he would dilute the Brotherhood's message. According to one Salafi, one new Islamist group – the General Islamist Current – held separate prayer sessions to the Brotherhood during Eid.

The Brotherhood denies negotiating with the military, but some sources suggest senior Brotherhood officials have contemplated a compromise that would see the camp disbanded in exchange for the release of senior Muslim Brothers from prison. But others warn that most at Rabaa – particularly those unaffiliated to the Brotherhood, or those whose relatives died earlier this month – would not stand for this.

"A large section of the Rabaa protesters, even those from the Muslim Brotherhood, would find any negotiation that fell short of the main demands a betrayal of the cause," said Salafi journalist Mostafa Sharky. "If this were to happen, these would creates massive divisions within Rabaa and the Brotherhood."

Rank-and-file Islamists at Rabaa refused to countenance the thought of the Brotherhood's leadership agreeing to a compromise. "No, no, no," said Aza Gala. "No one from the Muslim Brotherhood will agree to it. People died for this cause. If [the leadership] agree to these compromises, people will leave them."

Additional reporting by Marwa Awad