Saudi Arabia is a schizophrenic state oscillating between pragmatism and extremism.

Supposedly “moderate,” Saudi Arabia helps keep oil prices in check and expresses a readiness to sign a peace accord with Israel if the Israeli government fully accepts the Arab League peace plan, which was unveiled in 2002 and again in 2007.

As the price of oil drops from historic highs, Saudi Arabia — one of the world’s largest producers — keeps pumping and exporting crude rather than hoarding it. Which is not a bad thing, considering the fragility of so many world economies today.

As far as Middle Eastern politics are concerned, U.S. Secretary of State John Kerry has praised Saudi Arabia’s willingness to recognize Israel and stand up to Islamic radicalism, including Islamic State, which has captured wide swaths of territory in Iraq and Syria and committed crimes against humanity.

Bearing in mind Saudi Arabia, the Gulf states, Egypt and Jordan, Kerry said last month, “We’re seeing the potential emergence of a new regional alignment uniting countries with little in common but a shared aversion to extremism.”

Israeli Prime Minister Benjamin Netanyahu appears to share Kerry’s vision of a strategic alliance of nations united in the battle against Islamic radicalism. In a reference to the Arab Spring rebellions, which toppled long-established authoritarian regimes in Tunisia, Libya, Egypt and Yemen in 2010 and 2011, he said, “The collapse of the old order has made clear to pragmatic Arab governments that Israel is not the enemy.”

Yair Lapid, Israel’s former finance minister, appears to agree.

“We should turn to the Arab League and begin negotiations which will lead to a regional agreement and a separation from the Palestinians,” he said recently. “It’s an opportunity we must not miss. Egypt, along with Saudi Arabia, leads an alliance of moderate states — an informal coalition of Arab countries which share an interest in working with the West to stop the advance of radical Islam. Israel should be an integral part of that coalition, and we have a significant amount to contribute to that fight.”

Clearly, Saudi Arabia can play a key role in resolving the Arab-Israeli conflict and helping stem the tide of Islamic extremism, which surfaced in France with catastrophic results last week.

Yet we should have no illusions about Saudi Arabia. The House of Saud, a family business, is a reactionary absolute monarchy that belittles democracy, bans the construction of non-Islamic houses of prayer, forbids women to drive motor vehicles and funds schools with extreme Islamic curriculums that demonize Jews and Christians.

And lest it be forgotten, the Saudi Arabian regime is antisemitic. More than a week ago, the Saudi Ministry of Labor denied an Al Watan newspaper report that non-Israeli Jews would be eligible to receive guest worker visas for the first time.

“We bar entry only to those with Israeli citizenship,” Al Watan quoted a Labor Ministry spokesman as saying. “Other than that, we are open to most nationalities and religions. For example, if a worker is a citizen of Yemen but practices Judaism, the (Saudi) embassy (in Yemen) would not object to issuing him a work visa for the kingdom.”

Shortly after this statement was released, the Ministry of Labor issued a retraction, suggesting that Jewish guest workers are not welcome in Saudi Arabia, which plays host to more than nine million foreign workers, most of whom are Muslims.

Soon afterward, in another sign of Saudi Arabia’s mindset, Saudi Airlines — the national carrier — disclosed that separate seating will be imposed on male and female passengers on all flights in the future, though close relatives will be allowed to sit together.

Saudi Arabia may be, for now, an ally in the struggle against high oil prices and despicable organizations like Islamic State. The Saudis, too, may one day decide to establish diplomatic relations with Israel should conditions be right.

But before we get carried away by the rosy assumption that Saudi Arabia can be a useful player on the international stage, let’s remember that it’s still one of the world’s most unenlightened, backward and retrogressive nations.