Sorry if all this information is not all correct my focus is on wand lore.
The blood purists of the 90's had a lot of grief with Albus Dumbledore. The Dumbledore family was not noted in the Sacred-Twenty Eight, famously written by Cantankerus Nott in the 1930's, and so, in my opinion, that would have been a factor in their propaganda against the wizard. The list of the 28 dwindled until very few families were considered by society as 'pure blood', even if they were not technically. For a full definition of 'pure blood', I suggest you read this article which is absolutely brilliant.
Most significant was the famous pairing of Albus Dumbledore and Gellert Grindlewald. Rita Skeeter in her text 'The Life and Lies of Albus Dumbledore' argues that the relationship between Dumbledore and Grindlewald was "more than [met] the eye", and this may suggest homosexuality. However, Skeeter has been discredited by many, such as Elphias Doge who argued most vehemently against her information, claiming her to be a “nightmare of a woman”. Fans of Skeeter's work, including Muriel Prewett, are believed to have funded Skeeter’s book. Many, including Prewett, would have harboured resentment towards Dumbledore for his extreme pro-muggle leanings and may have paid the money for Skeeter to write such things against him.
Additionally, during the time of Voldemort’s reign, many people were murdered by the Death Eaters. Skeeter may have felt pressured by this to write harsh things against Dumbledore for her own safety (Chroniculus Punnet).
Now, here's where it gets a bit more interesting. Author J.K. Rowling has stated previously that Dumbledore was, in fact, gay, but there have been rumours flying around that her information was stated under the Imperius Curse (Garius Tomkink’s ‘JK Rowling: Friend or Foe?’). If this would be proved to be true, this would mean that her information is void and thus the perpetuation of Dumbledore’s sexuality is false. In my opinion, Tomkink is reliable. Tomkink’s previous texts on other notable witches and wizards such as Merlin and Godric Gryffindor are treated with extremely high acclaim.
We also need to look at why the blood purists would say he was a homosexual. After Gellert Grindlewald, who was against muggle supremacy over wizards, was sent to Nurmengard, Dumbledore began to align himself with pro-muggle ideals. He was strongly opposed by Voldemort’s followers who believed that wizards and witches were the supreme race over muggles and that muggle borns were thieves of magical knowledge. It is believed by many, including Hermione Granger, that the only thing stopping Voldemort from taking over was Dumbledore’s power.
After Dumbledore’s death at the hands of Severus Snape, the Anti-Muggle Act, set by the Muggle-Born Registration Commission in 1997 under Voldemort’s regime. In order to truly get the magical population to hate Dumbledore, Voldemort would logically need to set up negative propaganda against him. This was similarly done by Octavian against the witch Cleopatra and Mark Antony. Voldemort instilled fear of Dumbledore into the people by not only enforcing his anti-muggle past, but ALSO, by implying his homosexuality. At this time, as much as witches and wizards hate to admit it, they followed the same ideals as the muggles, in which members of the LGBT community were considered second class. Thus, by claiming that Dumbledore was gay Voldemort was able to make the population despise him more.
So in short, Dumbledore may have been gay, but from what we can see, there is serious evidence to suggest that this may have been propaganda against him, enforced by the blood purists.
No, we're pretty sure he was homosexual.
His behavior throughout his life firmly established he never had a romantic interest in women. The evidence pointing towards an early infatuation, or even romance, with Gallet Grindewald, although circumstantial, is far stronger than any evidence pointing towards any heterosexual relationships.
Further, I must add that modern analysis in disfavor of a homosexual Dumbledore is more in line with the Blood Purist agenda.