The tragic hanging of two “sodomites” in Iran may seem, in theory, like an obvious cause for U.S. concern and U.S. action. (Sign a petition! Demand human rights!) Yet in practice, those most attentive to LGBT concerns may be the least eager to pick this fight.

As Nina Strochlic reported in these pages Sunday, the two men, Abdullah Ghavami Chahzanjiru and Salman Ghanbari Chahzanjiri, were hanged in southern Iran on August 6, possibly for consensual sodomy. Their deaths are part of a wave of executions in Iran, with more than 400 in the first half of 2014 alone, according to the NGO Iran Human Rights.

We do not know for certain that they were executed for being gay—one Iranian source says they were, another is vague about their “crimes” but calls them “immoral villains.” If these men were hanged for consensual homosexuality, however, this could be another LGBT headache for the Obama administration, which has been trying to walk a tightrope between LGBT human rights on one end and international politics on the other.

Despite Iran’s state anti-Semitism, the recent arrest of U.S. journalists, and the continued oppression of women, the Obama administration has been attempting a rapprochement with the Iranian regime. Fending off Iran hawks in Congress and the D.C. punditocracy, the administration has argued for a policy of constructive engagement, pursuing diplomacy over military action to halt Iran’s nuclear program. The execution of two gay men, while it may not be surprising, certainly doesn’t make that “engagement” any easier.

Iran’s cooperation also is seen as essential to managing the chaos in Iraq and the Islamic State. With U.S. airstrikes against the Sunni militants, on-off (now definitely off) support of Iraq’s Shiite (ex-)Prime Minister Nouri al-Maliki, and the possible disintegration of Iraq, this cooperation—or at least not overt opposition—is surely of more strategic importance than the latest human rights abuse.

Conservatives who favor a hawkish foreign policy will claim otherwise, of course. In the topsy-turvy world that is international LGBT politics, Iran’s record on homosexuality is more a conservative cause than a liberal one. Just a few weeks ago, the House Foreign Affairs Committee held a hearing on human rights in Iran at which progressives such as Hossein Alizadeh of the International Gay & Lesbian Human Rights Commission testified about Iran’s hideous record of criminalization and persecution.

But at that same hearing, some of the most vocal defenses of human rights came from Robert George—the intellectual father of the right-wing “religious liberty” movement and, domestically at least, a zealous opponent of LGBT equality—and Republican Reps. Ileana Ros-Lehtinen, Chris Smith, and Ed Royce, who used Iran’s human rights record as evidence against the Obama administration’s policy of engagement.

To be sure, not allowing gays to marry is hardly the same as putting them to death. And Democrats as well as Republicans routinely criticize Iran’s repression of gays and lesbians. But the fact remains that when Iran persecutes gay people, conservatives in the United States suddenly become enamored of gay rights—and bash the Obama administration for not doing enough to defend them. Thus the administration is hit from all sides—at a moment in which it is trying to pursue its dicey diplomatic agenda.

The phenomenon of invoking LGBT equality as a justification for American foreign policies, which theorist Jasbir Puar calls “homonationalism,” has been around for several years. (Puar might prefer the term “imperialism.”) Even as conservatives fight LGBT equality at home, Puar says, they champion it overseas—as long as it serves their interests to do so.

Moreover, says Puar, Americans frequently impose their own conceptions of sexual and gender identity onto other cultures, stomping out indigenous ways of thinking about sexuality and gender, and perpetuating the myth that sexual diversity is a Western invention. Ironically, by demanding tolerance of “homosexuality,” Americans can inhibit the tolerance of forms of sexuality and gender identity that are long-standing traditions in non-Western culture.

For all these reasons, don’t expect the Obama administration, or the LGBT movement, to raise a hue and cry over this latest travesty of justice. As horrifying as this tragedy is, we might only be able to make it worse.