In 1971, or earlier, I read a short story in an anthology which has haunted me ever since, and I've spent years searching for it so I can re-read it. It was about a failed diplomatic mission or treaty negotiation between oxygen breathing races and non-oxygen (my recollection is fluorine or chlorine, but it could have been some other gas). The Oxygen diplomat is sharing the news, but isn't overly disappointed, putting a positive spin on the failed treaty discussions. What I recall is that he says that the other race shares an outsider perspective or different point of view, which in reality is a good thing which may be useful in the future. He does comment that the races are not in competition for the same planets.
"In A Good Cause -- " by Isaac Asimov, as mentioned in a comment by user14111.
Reprinted in "Nightfall and Other Stories" (1969). Originally appeared in 1951 in "New Tales of Space and Time".
Two friends, Dick Altmayer and Jeff Stock. Altmayer is an idealist and is imprisoned three times. Stock disagrees with his approach, and becomes a soldier, a commander, and then rises in Earth's government.
The story starts with a description of a statue to Altmayer. Then it proceeds to tell the story of each time Altmayer is imprisoned.
I believe you are remembering parts of discussions between Stock and Altmayer. One bit is from Altmayer's second brush with the authorities. The aliens are called the Diaboli and indeed need a different atmosphere. They have diplomats on Earth. Altmayer has a plot to kill them, which is foiled. He is arrested, and brought to the office of the secretary of Defense, his old friend Jeff Stock. They discuss their differences of approach to the Diaboli and to attempting to unite humans against them. Jeff points out in this conversation that they cannot live on human worlds; they need sulfide atmosphere and sodium sulfide oceans, as you mentioned in your question.
Another bit is from a discussion around his third imprisonment. This had to do with attempts to break up negotiations for uniting humanity -- under Diaboli arbitration. Both Altmayer and Stock actually wanted these diplomatic efforts to fail -- this was part of the overall diplomatic plan (perhaps your 'positive spin' on failed diplomatic negotiations).
A known quote from this story is "In a good cause, there are no failures. There are only delayed successes".
In the end, Stock is Earth's leader for many years, and leads in such a way that Altmayer's goals are achieved. But he led wars and even used Altmayer to disseminate forged documents to further the goals to get there. Humanity later is grateful to Altmayer, and will villify Stock who achieved his goals.