Words matter. Sensible people know that. But fanatics know it too.

Those who strive for peace between Israel and the Palestinians are keenly aware of their encirclement by radical propaganda. This has been true for decades, but the intensity of mania on the fringes isn’t abating: if anything, it’s only getting worse.

The phenomenon affects all who dare to advocate for Middle East peace, and therefore come under constant attack from a bizarre menagerie of extremists. What I had already perceived to be a generalized intensification of strident polemics was recently brought home to me directly as I found myself under unusually harsh attacks simultaneously from a twin set of zealots.

Last week, in an article on the right-wing pro-Israel website Algemeiner.com, Ben Cohen described me as “a faux moderate” because of articles I’ve written about Israel’s “Jewish state” demand. In a subsequent Twitter exchange, I pointed out that this can only mean that he’s calling me an extremist, an obvious truth he would neither admit nor deny.

Cohen’s imagination has constructed a binary world in which there are only two kinds of people: Zionists and extremists. It’s not enough that I seek peace between Israel and the Palestinians, and do not oppose Israel although I categorically oppose the occupation. Cohen can see that I obviously do not adhere to the ideological tenets or narrative of Zionism. And, for him, by definition that makes me an extremist.

At roughly the same time, the anonymous abusive and spamming Twitter feed that calls itself “@Ikhras” – though one can certainly make an educated guess as to at least some of the people involved – decided I was not simply a “right-wing Zionist,” which already they call me almost daily: they declared I was actually “the most right-wing of all these Zionists,” in reference to a debate I am having later today with Rabbi Shmuley Boteach, the decidedly right-wing Wall Street Journal Foreign Affairs columnist Bret Stephens, and noted liberal commentator Peter Beinart.

It’s laughable. For the likes of Cohen, because I’m not a Zionist but rather an Arab who wants peace with Israel, I’m a “faux moderate.” For @Ikhras, whoever is cowering behind its craven anonymity, because I want peace with Israel, even though I’m not a Zionist, I’m more “Zionist” than three self-avowed Jewish Zionists, and more “right-wing” than one of America’s most prominent conservative columnists.

Indeed, over the past few months I’ve been inexplicably described by the far left as an “Arab neoconservative,” simply as an empty pejorative since I can’t think of any policy view I hold, on either domestic or international affairs, that can honestly be described as right-of-center.

For the extremes, though, there is no center ground. There is no way to agree to disagree, or even partly agree. Their narratives are hewn in marble; any disagreement can only be a manifestation of willful wickedness, a vile betrayal of self-evident Truth and Justice. If you don’t agree with them completely on everything, you’re not only ipso facto a bad person: more importantly – because there is no room for genuine moderation – you must also be a fanatic on the other side. Thus it was that in the past few days on Twitter I could be simultaneously described as both “a faux moderate” and “the most right-wing Zionist.”

I recently received copies of two new books that illustrate exactly the same phenomenon. Coming from what appear to be radically different positions, they actually agree on a vast number of issues and echo each other’s mentalities perfectly. Both derisively and angrily dismiss the international consensus in favor of a two-state solution and advocate a one-state “solution.” And they share far more in common than just that.

Caroline Glick’s The Israeli Solution: A One-State Plan for Peace in the Middle East and Ali Abunimah’s The Battle for Justice in Palestine clearly stake out the same position, but in mirror image to each other. Both insist that only Jews or Palestinians, respectively, have national rights and rights to self-determination in the land between the river and the sea. Both insist that a single state is achievable and necessary, and will be a happy and peaceful polity as long as it is under the majority rule of their own community. Sure, the other side may have to endure some sacrifices. But ultimately they might well, or at least should, be happy with the outcome. And if not, tough: Justice demands it.

There is no room in either book for the ideas that compromise is essential, that peace is an important value, that the other side has any respectable case or legitimacy whatsoever, or that their own side has any difficult choices to make other than simply asserting the indisputable moral authority of its own maximalist cause. For all of their manifest differences, the two books are indistinguishable at the latent level. They are, in effect, exactly the same book.

You’d think this might make Glick and Abunimah, or at least some of their fans, think twice. But righteous zeal may prevent many of them from seeing past the tissue-thin, surface level, polar opposite appearances and recognizing the underlying interchangeability and complementarity of their arguments and mentalities, which aren’t just barely concealed but are actually strikingly obvious.

Anyone who follows the news will know certain high-ranking Israeli and Palestinian officials have recently been making statements that strongly encourage maximalism and discourage compromise and moderation. This isn’t new, of course, but it appears to be approaching a piercingly shrill crescendo as US Secretary of State John Kerry’s peace initiative comes to a head.

Highly counterproductive statements by senior officials are more damaging than books by demagogues, which in turn are more harmful than blog postings and tweets by fanatics. But all of this angry bombast should remind those of us who are committed to a future of peace and dignity for both Palestinians and Israelis, based on an end to the occupation, that we are surrounded on all sides by cynical manipulators and wild-eyed zealots.

To overcome this widespread rhetorical offensive against ending both the occupation and the conflict, we will all have to work together more closely than ever to marginalize extremism and empower moderation, while remaining cognizant of our differences and not pretending they don’t exist. Our words – the words of peace – must prevail.