TURKEY – Passports are nearly indestructible objects. An American-Israeli friend of mine discovered this in an Iraqi farmhouse when she frantically tried to get rid of her Israeli passport before her identity could be discovered by the Shia insurgents who had detained her and other journalists on the outskirts of Baghdad. She tried to set fire to it, but it wouldn't burn. She tried to flush it down the toilet, but the primitive plumbing couldn't handle it, not even when she finally managed to rip the document into separate pages. Finally, she found a way to hide it which I shouldn't detail here.

Traveling with two different travel documents, you get used to putting each one in a different spot and using the right one at the appropriate time and place. If you are in a Muslim country with an Israeli passport and another, Western one, the blue booklet with the Menorah symbol will usually stay hidden deep in your bag, and when asked for identification you will automatically pull out the more acceptable passport.

When plain-clothes police asked who I was on a street corner in the working-class neighborhood Armutlu of Antakya, a mid-sized town in southern Turkey near the Syrian border, I instinctively presented my British passport. They were suspicious of any outsider; Prime Minister Recep Tayyip Erdogan had just appeared on television accusing "foreign interests" of fomenting the protests around the country and claiming Twitter was "a threat to society." Here was a foreigner holding a tablet computer on the outskirts of a violent demonstration.

Usually in these situations, just the sight of the royal seal embedded on a British passport – with the exhortation of "Her Britannic Majesty's Secretary of State" inside "to allow the bearer to pass freely without let or hindrance" – immediately does the trick. It didn't cut it in this case. Something about the visas and entry stamps (or lack thereof) bothered them, and they continued to badger me for more identification.

You don't want to disoblige police officers in Turkey, especially not on a street where their colleagues are pointing loaded machine guns at civilians and lobbing tear gas grenades at them, but I wasn't sure how best to get out of the situation. I told them I had the rest of my documents back at the hotel, which only made them more suspicious.

Luckily, a local friend turned up at that moment. "I have another passport," I told him, "my Israeli one. What do I do?" He looked at me as if I was a simple child: "An Israeli passport is never a problem here. Give it to them immediately." I had no choice but to trust him, and I extricated the passport from my bag's inner compartment.

The police officers' attitude immediately softened. They allowed themselves to smile, and there was respect in their voices. One of them said to me, "I don't believe you don't understand Turkish" (I know what he said because my friend interpreted for me). They gave me back my British passport – they had no interest in it any longer – passed the Israeli one around, laboriously wrote down its details, and five minutes later they let me go with a friendly warning not to stick around in the neighborhood that was rapidly becoming an urban battlefield.

Walking back to my hotel, I was at first too relieved to think about the meaning of what had just happened. Relieved and amused that in Turkey, of all places, an Israeli passport had proved more trustworthy than my royal-issue British travel document.

Later that night, I went online and read some of the Israeli coverage of events in Turkey. The glee of the tabloid press was barely concealed. For the last few years Prime Minister Erdogan has been portrayed in the Israeli media, with some justification, as an Islamic, Israel-hating hardliner, eager to build his relations with the Arab world and Iran at the expense of Turkey's once strong strategic relation with Israel and the West. Finally he was getting his comeuppance at the hands of the silent secular majority, and a return of a more friendly Turkey was just around the corner.

If that is the case, how could I explain the graffiti around Istanbul's Taksim Square calling Erdogan a "Zionist"? And why were the police, the grim face of Erdogan's government, so friendly when they realized I was an Israeli?

These things, of course, are never so simple. The ties and tensions between Turkey and Israel run much deeper than passing political combinations. Even at the height of the strategic alliance, things were not always rosy. And the relationship with the Jewish state was always connected to the 2000-year presence of a small but proud Jewish minority in the Ottoman Empire which prospered for generations in between periods of bloody persecution.

Religious and national labels are extremely ambiguous and almost never what they seem. A colleague based in Istanbul said to me this week that "Erdogan and his party are religious Muslims, but they are not Islamists. They have not tried to establish sharia law. It would be much more accurate to call them religious conservatives; they are not radical."

These descriptions are difficult for an outsider to understand when Erdogan's foreign policy over the last two years has involved trying to cozy up to the Muslim Brotherhood in Egypt and Hamas in Gaza. But then, how difficult it is to understand the various groupings of Jews and Israelis along religious, political and societal lines?

Are Israeli settlers radical extremists or religious conservatives? What is the difference between being a conservative Jew in the United States and in the United Kingdom? Why do some Sephardi Jews in the West proudly call themselves "Jewish Arabs," and why do many Sephardim in Israel hate Arabs "because we know what they are really like"?

Turkey, with its beguiling kaleidoscope of identities (Muslim, but not Arab like its neighbors), its proud Islamic tradition alongside muscular secularism, its insistence that it is a democracy but with distinct authoritarian tendencies, and its eternally shifting attitudes toward the Jews and Israel – all these challenge us to question our view of ourselves and others, and remind us that our identities can never be summed up just by the color of our passports.