Sulivan describes Gänswein's relationship with the Pontiff as "intense" and takes particular note of the fact that Gänswein regularly takes two meals with Benedict XIV and accompanies him on a walk around the Vatican grounds. That and the emeritus Pope's habit of wearing red Prada shoes with his Papal robes, leads Sullivan to hint, not at all subtly, that Benedict XIV might be gay and somehow involved with his secretary. Sullivan goes so far as to verbosely state that Gänswein is "in some kind of love" with his boss.
Indeed, were Benedict XVI a CEO of some high-flying American company, Sullivan's speculation might be dead on. The shoes are a little weird, the closeness of the secretary does seem a touch off, and no less than Donatella Versace has used Gänswein as an inspiration for a fashion catalog... so Toibin may have a point about his looks.
But a reality check is also in order. The Pope's shoes are red by custom and liturgical mandate and while our current version of them may look ridiculously flamboyant the indoor papal slippers of red velvet or silk and adorned with gold braid that were common in the Church's earlier days were a good deal more over the top. Indeed, almost every Pope in living memory has worn those flashy red shoes to some extent, though John Paul II ditched them for a pair of brown loafers.
Gänswein has seemed to shadow the Pontiff these last few years but then again, the Pope is also not only the head of the Church but also the head of a sovereign state. While the Catholic Church may be the world's oldest bureaucracy it is far from the largest with just 836 residents in the Vatican to oversee the day to day operations of a Church and state that serves something like 1.2 billion people. The man has a lot on his plate and a very small staff; no wonder his secretary is always around.
As for Gänswein's looks? Well the Italian version of Vanity Fair apparently ran a photo of him on their cover without either his or the Church's permission. When Vanity Fair is willing to feature you on their cover and do it without asking permission, there's not much more one can say on the topic. I'll spot Sullivan that point.
The bottom line is that it is exceedingly unlikely that Benedict XVI is gay and even more unlikely that he had some kind of clandestine relationship with his secretary. Sullivan seems to fall into the tacit trap that a lot of American journalists do when writing about the Papacy. They use the Presidency as a sort of mental model for the Pontiff's office and make a number of assumptions about the politics of the Church based upon that assumption.
But the Presidency isn't a suitable model for the Papacy nor, really, is a Monarchy or even a Dictatorship. The Pope is something unique -- at once an absolute monarch with complete and total control over the Vatican's affairs of state and a spokesperson for God. Catholic dogma holds the Pope to be capable of speaking ex cathedra meaning "form the throne [of Peter]" and in so doing, invoking Papal Supremacy. The long story of that invocation made very very short is that the Pope can effectively retcon anything he wishes into Catholic dogma.
Were Benedict XVI involved in a long-standing and committed relationship with his secretary he'd have no reason to hide it. Were he a Cardinal or a Priest that would be something very different, but as Pope he has/had the power to rewrite Catholic doctrine with a word.
If Benedict XIV really were the closeted gay Pontiff that Sullivan suggests, why allow Catholic dogma to continue to condemn homosexuals? Why remain closeted? Why give up the power to make these changes to the faith? It seems contradictory to hold the view that Benedict XVI was craven enough to maintain a secret homosexual tryst in full view of the entire world and in defiance of church law while simultaneously holding the view that he was too dedicated to the Church and Papacy to use it to absolve himself.
Far less complicated and far more likely is the presumption that Pope Benedict XVI is not gay but is, in fact, a very strange, very shy, very insular man who was never terribly comfortable with the public duties of the Papacy. He leaves it as he entered it: awkwardly and with a very few friends that he really and truly trusts.