Trump reacted with hilarity to the news that the Ayatollah might be gay. How might previous American presidents reacted?

Each president would have filtered the intelligence through his own coalition logic, personal temperament, and the specific political moment he occupied.
Franklin Roosevelt would probably have found it useful and filed it away without laughing. He was a ruthless collector of personal information about rivals and allies alike. J. Edgar Hoover kept files on everyone partly because Roosevelt created a culture where personal vulnerability was understood as a political resource. FDR would have seen the intelligence as potential leverage and said nothing publicly, possibly nothing privately either, because discretion about that kind of information was how you kept it useful.
Eisenhower would have been uncomfortable. He came from a military culture with its own complicated and largely suppressed relationship with homosexuality, and he would have understood immediately that the information was both a potential weapon and a liability if mishandled. He would have passed it to the CIA and told them to determine its operational value. His reaction in the room would have been a flat midwestern silence followed by a question about verification.
Kennedy would have smiled. He had enough of his own private life to protect that he would have appreciated the irony without moralizing about it. He also had a sophisticated enough sense of how information moved through political systems to understand its propaganda potential. He would have asked McGeorge Bundy what they could do with it and whether it could be used to split the Iranian leadership internally.
Johnson would have been loud about it in private and disciplined in public. He was famous for crude humor and for using personal information about rivals mercilessly in backroom settings. He would have made jokes that cannot be repeated here and then asked his national security team how to weaponize it without fingerprints.
Nixon would have been the most strategically serious about it and also the most personally conflicted. He was deeply uncomfortable with homosexuality, made that plain on the White House tapes, and would have reacted with genuine disgust before his strategic brain engaged. Then he would have thought carefully about whether it could be used as part of a broader destabilization effort. Nixon understood psychological warfare better than almost any postwar president. He would have wanted to use it but worried about the blowback if the operation were traced back to the White House.
Carter would have been visibly uncomfortable for entirely different reasons. His Baptist faith made him genuinely conflicted about homosexuality throughout his life, though he consistently moved toward greater acceptance over the decades. In the late 1970s context he would have worried about the ethics of using a man’s private life as a weapon, asked whether it was consistent with American values, and probably frustrated his national security team by insisting on thinking it through morally before acting on it strategically.
Reagan would have deflected with a joke that was gentler than Johnson’s but served the same function of not engaging seriously. His public persona required optimism and a certain avoidance of anything squalid. In private his reaction would have depended heavily on who was in the room. With Bill Casey at the CIA the conversation would have turned operational quickly. With Nancy present he probably would have moved on fast.
George H.W. Bush would have been the most classically WASP about it, meaning a brief acknowledgment, no visible reaction, and an immediate pivot to what the intelligence community recommended doing with the information. He was a former CIA director. He understood that personal information about foreign leaders was a tool, not a subject for personal reaction. His affect in that briefing room would have been almost unreadable.
Clinton would have reacted with genuine intellectual curiosity and probably spent twenty minutes asking about the sourcing, the cultural context, and the theological implications before anyone could steer him back to the policy question. He also would have been acutely aware, sitting in that room, of the particular irony of a leader being politically vulnerable because of private sexual behavior. Whether that awareness would have made him more or less inclined to use the information is an interesting question.
George W. Bush would have been uncomfortable in a specifically evangelical way. By his second term he had anchored much of his political coalition to social conservatism, and homosexuality as a topic carried enormous political charge in that context. He would not have laughed. He would have looked to Cheney, who would have shown no reaction whatsoever, and to Condoleezza Rice, who would have immediately reframed it as a question of regional stability. Bush would have followed her lead.
Obama would have had the most complex reaction in the room and shown the least of it. He was personally comfortable with gay people and had evolved publicly on marriage equality by his second term. He also had a lawyer’s instinct for not reacting to raw intelligence before it was verified. His visible response would have been thoughtful and measured. Privately he would have been alert to both the propaganda potential and the risk that using it would undermine the kind of multilateral legitimacy he spent his presidency trying to build. He would have asked whether American fingerprints on the story would damage relationships with Muslim-majority allies.
Trump laughed, which is in some ways the most honest reaction in the room. He was not performing strategic calculation or moral deliberation. He found it funny and said so. That transparency is consistent with everything else about how he processes information. The laugh also signals something Alliance Theory predicts, that he immediately understood it as a status weapon rather than as a piece of intelligence requiring careful handling. The humor was recognition. He knew exactly what it was for.