What are some common misconceptions about this deity?
There are two answers that come to mind immediately on considering this question. The first, which one sees even in some academic sources, is that Antinous was divinized by Hadrian out of grief and devotion for him. This is simply not the case. Antinous was divinized because he drowned in the Nile. Osiris had become lord of the underworld by dying in the same way, so anyone who shared his death shared his divinity. Many humble ordinary people over the millennia had been deified in that way; Antinous would have been just another of them, served by a local priesthood until his memory died out, if he had not happened to be the beloved of an extremely powerful and wealthy person.
What Hadrian did do was build a city where his beloved’s body was found, endow his priesthood, and promote his worship. It seems to have spread rapidly, even allowing for Hadrian’s influence. It’s because of Hadrian that we have so many surviving images of Antinous, all of them recognizably the same person. It’s because of Hadrian and those who chronicled him that we have Antinous’ name and birthplace, know about their relationship, and know how intensely Hadrian mourned his death. But he did not simply declare his beloved divine, or compel the Senate to do so, in the same way that deceased emperors and their spouses and other relatives were declared divine. Antinous was sometimes called a hero, sometimes a daimon (that is, a spirit), and most often a god, deus or theos, but not divus, like Julius, Augustus, or Hadrian himself.
The second very common misconception about Antinous is that he was and is “a gay god”, or “the gay god”, or “the god of gayness”. I think this is largely a misunderstanding of how sexuality was perceived in the ancient world. Heterosexual and homosexual are concepts not more than 150 years old. Gay as a sexual identity and a subculture is newer than that. From our 21st century perspective, a great many men in ancient Greece and Rome were not gay, but bisexual; they married and fathered children, but also carried on intense emotional and sexual relationships with other, normally younger men. Hadrian entered into a political marriage as part of his rise to Emperor; he remained married to Vibia Sabina, but he was known to have affairs with both women and young men. Whether a great many women followed in the footsteps of Sappho and had passionate affairs with other women while also being dutiful wives and mothers is not recorded (but I like to think they did). The important thing, from the dominant male standpoint, is that the wife was not presenting her husband with children he had not fathered to inherit his name, status, and property.
Certainly Antinous blesses erotic and romantic relationships between men and supports the legal and social acceptance of those relationships. But he seems to have a broader interest in honest erotic and romantic relationships generally, no matter what the combination of genders, and in issues of social justice and equality, whether confined to gay men or queer people or not. Like Dionysus, he is interested in personal and social freedoms, joy and ecstasy, theatre and performance. Like Hermes, he is interested in language, communication, and connection; he also, like Hermes, can be a psychopomp and guide of the dead. Like Apollo, he is interested in healing, in music and poetry, and in oracles and prophecy.
You do not have to be a gay man to worship Antinous. He will not turn you away if you are not. He has much to offer devotees who are interested in any or all of the things that concern him, to anyone who is moved by his beauty. Come to him with a prayer and a simple offering, and he will show you that he is not only beautiful, but benevolent and just.