On Tuesday, soon after two young Palestinian men hacked their way through a Jerusalem synagogue, leaving four dead rabbis and a dying police officer in their wake, the Popular Front for the Liberation of Palestine announced that the perpetrators were from its ranks and praised their “heroic operation”. Although armed with a pistol, the two murderers chose to use meat cleavers for their bloody work – Isis-style.

The PFLP once portrayed itself as a staunchly secular, Marxist-Leninist liberation movement. Founded by a Christian doctor, it even had a handful of radical anti-Zionist Jewish supporters. PFLP today is a shadow of its former self and no ally of Islamic State (Isis), seeking instead the patronage of Isis’s mortal enemy, the Islamic Republic of Iran. Hamas, which has also been at pains to distance itself from Isis, also rushed to congratulate the synagogue murderers.

Celebratory images of blood-stained cleavers, popularised in Isis beheading clips, quickly flooded many Palestinian websites and Facebook pages. It did not matter that the chosen targets were elderly civilians inside Israel’s pre-1967 borders.

This is what a religious war looks like, and we should stop kidding ourselves that this is not what has been happening in the Middle East. In various degrees it’s been going on for a century. Yes, it is also a conflict over a piece of land between two nations, and not all Israelis and Palestinians – hopefully still a minority in both societies – want to see this as a struggle between Muslims and Jews, but there are enough of them who do.

It may have been easier to portray the earlier decades of the Palestinian conflict as a territorial dispute between Zionism and Arab nationalism. The fact that the founders of political Zionism were resolutely secular – most rabbis at the time remaining deeply suspicious of a movement seeking to pre-empt the Messiah – contributed to this view of the conflict. But religion was always a significant motivating force on both sides.

The first major clashes in the last century between Jews and Muslims in the Holy Land were not sparked by the establishment of new Jewish agricultural settlements, but by disputes over prayer rights at the Western Wall in Jerusalem. They are reminiscent of current suspicion among Palestinians of Jews seeking today to pray within the Temple Mount compound, harbouring dreams of supplanting the Haram al-Sharif mosques with a third temple. Today’s fashionable talk of Zionism as colonialism was to come much later.

Not that Zionism was ever a totally irreligious movement. Theodor Herzl may have been born into an assimilated Viennese family, and David Ben-Gurion along with his fellow pioneers ditched religious stricture, but they still used the Bible as their deed of ownership to the ancient homeland, and clung to their ancestry while other Jews embraced internationalist communism. For a few decades, while various forms of nationalism and socialism remained popular among Arabs and Jews alike, both sides could claim that they were secular liberation movements and that their battle was over disputed territory. But they could not keep the charade up for long.

The ascendancy from the 70s onwards of the religious settler movement in Israel, and the rise of Hamas and other overtly Islamist Palestinian movements in the late 80s, were clear signs not only of the weakening of secular forces in both societies, but that the language of the conflict was returning to its roots.

Tuesday’s attack in Jerusalem may have been the first of its kind in living memory on a neighbourhood synagogue in the capital, but Palestinian organisations carried out similar murders in European synagogues in the early 80s. At the same time a Jewish underground was storing explosives and preparing for an apocalyptic attack on the Jerusalem mosques, which was foiled by the Shin Bet security service. The most recent atrocity to resemble this week’s murders was the Cave of the Patriarchs or Ibrahimi mosque massacre (in a religious war, what you call an atrocity is also determined by your religion) in 1994, when Baruch Goldstein gunned down 29 Muslim worshippers during morning prayers.

Israelis argue they are not pursuing a religious war against Muslims – Goldstein was a member of a small racist party that was swiftly declared an illegal terror organisation, Israel’s security services are trying to apprehend like-minded vigilantes who are torching mosques, and the great majority of Israelis abhor such actions – while even a cursory glance at the Palestinian media reveals a glorification of attacks against Jews.

The Palestinians, from their side, deny they are simply out to kill Jews, and demand that the world see the murders in the context of the ever-increasing frustration of a young generation living under unending Israeli occupation and oppression. That is the sole root cause of violence, they insist.

Most Israelis still want to believe they are fighting only for their security and have nothing against Muslims, while many Palestinians still want to blame the occupation for all violence; but it is increasingly becoming self-delusion, kept up partly for western consumption. The political leaders and talking heads sought out by the media are still usually secular, couching their arguments in palatable English terms. Meanwhile on the fighting lines, where an Israeli colonel in the summer exhorted his troops about to go into battle to “exterminate the enemy which is abominating the God of Israel”, and mainstream Palestinian websites now regularly feature cartoons of van-driving Shahids protecting al-Aqsa by running over hook-nosed kippah-wearing Jews, with beards and side-locks, the language is unambiguously religious.

The two sides’ current leaders are outwardly secular men. But neither Prime Minister Binyamin Netanyahu nor President Mahmoud Abbas have been above using religion in recent weeks to prop up their flagging constituencies. Abbas, in a speech two weeks ago, warned of religious war, and with the same breath accused Jews of defiling the Jerusalem mosques. Netanyahu accuses Abbas of inciting terror attacks and, yes, a religious war, but is pushing through laws that will establish the “Jewish identity” of the state as superior to its democratic principles. Neither wants violent escalation, but religious feelings are too potent not to be used.

In May, Pope Francis, the global religious leader even atheist liberals love, summoned presidents Shimon Peres and Abbas to Rome for a joint prayer for peace. Barely a month later the latest round of bloodshed in Gaza began. It’s hard to blame Francis for this pointless PR exercise: if he had invited the sheikhs and rabbis who are the real movers in the wars of hate they would have turned him down. But by feting two cynical politicians who have sought to harness religious feelings for their own agendas, as Abbas is doing now with the furore over the Jerusalem mosques and Peres did nearly 40 years ago – when, as defence minister, he authorised the first settlements in the West Bank, in the hope the settlers would support him against his rival Yitzhak Rabin – the pope helped perpetuate the myth.

Accepting that the Israel-Palestine conflict is also a bitter religious war runs counter to the international community’s preferred solutions. But it would be better to recognise this awful fact, which is a central reason that none of these solutions have worked, despite the intense diplomatic efforts to resolve the conflict.

Above all, acknowledging the extent to which both Israeli and Palestinian leaders are exploiting religious feelings would be a step towards holding them accountable for the actions of the extremists within their own camps.