Another note. Nietzsche’s tone, when it comes to instincts, talks about power, which is very similar to Hitler’s tone in ‘Mein Kampf’ (getting power over masses, having learned techniques to manipulate the masses which are seen as weak and feminine, waging a war against a spirit of weakness manifested through lack of conviction, undecisiveness, etc). Plato’s tone seems to address more a concern about restoring the order inside the soul, according to reason. On reason, Nietzsche noted in another of his writings (The Twilight of the Idols, The Problem of Socrates, 10):

When one finds it necessary to turn reason into a tyrant, as Socrates did, the danger cannot be slight that something else threatens to play the tyrant. Rationality was hit upon as a savior; neither Socrates nor his “patients” had any choice about being rational: it was necessary, it was the last resort. The fanaticism with which all Greek reflection throws itself upon rationality betrays a desperate situation; there was danger, there was but one choice: either to perish or — to be absurdly rational. The moralism of the Greek philosophers from Plato on is pathologically conditioned; so is their reverence for logical argument. Reason equals virtue and happiness, that means merely that one must imitate Socrates and counter the dark appetites with a permanent daylight — the daylight of reason. One must be clever, clear, bright at any price: any concession to the instincts, to the unconscious, leads downward.

But the previous paragraphs are equally interesting:

8

I have explained how it was that Socrates could repel: it is therefore all the more necessary to explain how he could fascinate. That he discovered a new kind of contest, that he became its first fencing master for the noble circles of Athens, is one point. He fascinated by appealing to the competitive impulse of the Greeks — he introduced a variation into the wrestling match between young men and youths. Socrates was a great erotic.

9

But Socrates guessed even more. He saw through the noble Athenians; he saw that his own case, his idiosyncrasy, was no longer exceptional. The same kind of degeneration was quietly developing everywhere: old Athens was coming to an end. And Socrates understood that the world needed him — his method, his cure, his personal artifice of self-preservation. Everywhere the instincts were in anarchy, everywhere one was within sight of excess: monstrum in animo was the common danger. “The impulses want to play the tyrant; one must invent a counter-tyrant who is stronger.” After the physiognomist had revealed to Socrates who he was — a cave of bad appetites — the great master of irony let slip another clue to his character. “This is true,” he said, “but I mastered them all.” How did Socrates become master over himself? His case was, at bottom, merely the extreme case, only the most striking instance of what was then beginning to be a epidemic: no one was any longer master over himself, the instincts turned against themselves. He fascinated, being an extreme case; his awe inspiring ugliness proclaimed him as such to all who could see: he fascinated, of course, even more as an answer, a solution, an apparent cure [therapy] for this disease.

Nietzsche, on the other hand, wrote against democracy because he thought democracy embodies the ‘spirit of the herd’ and it leads to general mediocrity by means of tyranny of the stupid and common. Nietzsche praised the spirit of nobility, he thought imbalance of instincts is the given state of nature and the best human specimens are those who rise above them by using them, not by denying them. He believed in the power of instincts and thought that the powerful do not deny their instincts, but use them to their advancement, to fulfil their ‘power to will.’ He cited as great examples of such achievement the Athenian general Alcibiades, Roman leader Julius Caesar and Italian artist Leonardo da Vinci. All of them, he argued, asserted themselves in a time when the democratic, flaccid type of human was prevalent (Beyond Good and Evil, 200).
This is just an example of many passages dealing with the spirit of weakness that Nietzsche thought was characteristical of democratic times:

The UNIVERSAL DEGENERACY OF MANKIND to the level of the “man of the future”–as idealized by the socialistic fools and shallow-pates–this
degeneracy and dwarfing of man to an absolutely gregarious animal (or as they call it, to a man of “free society”), this brutalizing of man into a pigmy with equal rights and claims, is undoubtedly POSSIBLE! He who has thought out this possibility to its ultimate conclusion knows ANOTHER loathing unknown to the rest of mankind–and perhaps also a new MISSION!
(Beyond Good and Evil, 203, 30-35).

The emphases are Nietzsche’s.
As I have argued elsewhere on this blog, Hitler did not seem concerned with rooting out a certain sexual orientation out of humanity as much as with a spirit of weakness that he thought was prevalent in the society of his own time.

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So if one is so bold to claim that Nietzsche’s alleged homosexuality had a backdoor influence on his writing and thus motivated a political elite to rise to power and build a Nazi regime, then it can be equally credible to say that Plato’s homosexuality had an influence on his treatment of instincts in his philosophical writings, to the extent that it influenced early Christianism.