Sorry to burst everyone’s branding bubble, but there is a “Jewish lobby.” It happens to be pro-Israel because it’s Jewish — not the other way around.

Jews don’t like hearing non-Jews use the term in public, and perhaps they shouldn’t. But as an interest group, Jews as such are ably represented (most of the time) by a close-knit network of advocacy organizations. Most of these are purely or predominantly Jewish, judging by their branding, supporters and staff. Evangelical organizations, the labor movement and millions of individual Americans also support Israel, but they have not initiated — nor do they currently control — the pro-Israel movement.

The Conference of Presidents of Major American Jewish Organizations was founded decades ago as a clearinghouse for American Jews to connect with the executive branch on Israel. American Jewish Committee, Anti-Defamation League (ADL), Simon Wiesenthal Center — these mainstream Jewish organizations are the ones out front, with the Republican Jewish Coalition riding shotgun, raising concerns about Pentagon nominee Chuck Hagel’s pro-Israel credentials. They have also been insisting that Hagel’s sole reference to the “Jewish lobby” was out of line.

The American Israel Public Affairs Committee (AIPAC) has remained silent on Hagel, and wisely so, given that AIPAC must focus on the bottom line of American financial aid and strategic cooperation and not be seen as the Jewish lobby. But at its core, that’s what it is.

Sure, AIPAC has done important outreach and coalition building with Christian groups and minority demographics across the country, but its membership and staff are overwhelmingly Jews, and no non-Jew has ever served in a leadership capacity, whether lay or staff. And that’s OK. If Evangelical Israel-lover Rev. John Hagee suddenly became the president of AIPAC, its membership rolls would nosedive overnight.

Even when asked specifically about AIPAC over some single malt after Sabbath services, the average synagogue-going Jew will affirm that it’s “our lobby” and even “the Jewish lobby” as much as “the pro-Israel lobby.” And when a member of Congress is informed of a meeting with a “pro-Israel” delegation, that usually is understood to mean Jews and their rabbis.

Can we ever get used to it? After 20-plus years in Washington, I have. I am not ashamed by it, and I am very careful about throwing around the anti-Semitism card, especially in public.

On Capitol Hill, there’s a well-publicized caucus for nearly every group of members imaginable, from Latinos and Asians, to women, African-Americans, bikers and dairy supporters. But although the few dozen Jewish members of Congress meet periodically, they do so largely below the public radar and without an official cachet. The idea of a “Jewish Caucus” is still considered too dangerous to put out there, given our continued sense of vulnerability and the persistence of minor but endemic anti-Semitism. Substantively, there is nothing wrong with American Jewish elected officials coordinating their ideas and actions on behalf of common concerns, like any other group. And yet, to us, there is. Something reminds us of “The Protocols of the Elders of Zion.”

Given our collective phobia, it would be relevant to know who — if anyone — from the Jewish lobby reached out to Hagel after his single mention went public. What was his response? Or was there no outreach at all, for fear of aggravating the situation? Well, we’ve sure aggravated that situation now.

As the “Jewish lobby,” we have a clearly vested interest on Israel, while “pro-Israel lobby” messages that what’s good for Israel is good for America — can’t be any more patriotic than that. … Yet, as American Jews, we are fully within our rights to openly pursue our own interests while also persuading others that Israel really is good for America.

Jews happen to have a hang-up about this, but that doesn’t mean violators “border on anti-Semitism,” as ADL chief Abe Foxman told The Washington Post’s token neo-conservative blogger. Having taken the bait on Hagel’s “Jewish lobby” comment, Foxman put the very question of Jewish influence on the table, out in the open. By making Chuck Hagel’s “Jewish” problem a matter of concern, major Jewish organizations have opened the very controversy they’ve been warning us against.

Ironically, it was precisely the “Jewish” organizations which objected to the term “Jewish lobby” after Hagel’s nomination became likely. The so-called “Israel” (or better, “pro-Israel”) lobby has stayed away, at least officially.

And this must also be said: How is it possible for the Anti-Defamation League to publicly call someone a borderline anti-Semite, and then credibly claim it does not necessarily oppose his nomination to the president’s Cabinet?

Shai Franklin, a senior fellow with the Institute on Religion and Public Policy, has been an executive with several Jewish organizations. Twitter: @shaifranklin.