Google coughed up some useful answers. It appears that because of the scandalous subject matter of some of Reed's songs for the Velvet Underground, many people assumed that Reed must be gay. And you know what happens when you assume.
There was a widely circulated claim that Reed was subjected by his family to electroshock "therapy" as a teenager because he was gay. His sister has denied this, admitting the electroshock but denying that it was because he was gay.
During Lou’s teenage years, it became obvious that he was becoming increasingly anxious, avoidant and resistant to most socializing, unless it was on his terms ... Verbal fights between Lou and my parents erupted — about going into the city to play band dates, about the dangers he might confront. My parents were frightened, upset, and bewildered ... Lou was not able to function at that time. He was depressed, anxious, and socially unresponsive ...
So, you see, it was all the doctors' fault. And no doubt it was. I'm not sure I believe her completely, since as she says the family "absolutely never spoke about the treatments, then or ever." Homosexuality in most of American culture in those days was unspeakable, so there's no reason to believe that she'd know if it was a factor for their parents. So much of the piece sounds like the familiar denial that one's family, one's parents, could ever have done something bad. But it does seem that the confident and casual claim I kept encountering, that the ECT was meant to burn out the gay, is based on rumor and has never been verified.It has been suggested by some authors that ECT was approved by my parents because Lou had confessed to homosexual urges. How simplistic. He was depressed, weird, anxious, and avoidant. My parents were many things, but homophobic they were not. In fact, they were blazing liberals. They were caught in a bewildering web of guilt, fear, and poor psychiatric care. Did they make a mistake in not challenging the doctor’s recommendation for ECT? Absolutely. I have no doubt they regretted it until the day they died. But the family secret continued. We absolutely never spoke about the treatments, then or ever.Our family was torn apart the day they began those wretched treatments ...
It was only years later that I learned that the teenage Lou, like me, had spent time in mental hospital as a result of his “homosexual tendencies”.
It’s 1959 and Louis Allan Reed is acting up. If it’s not the 17-year-old’s mood swings or the bad grades, it’s his recent displays of homosexual behavior. At their wit’s end, his parents give him what any other strict, conservative Jewish parents in middle-class Brooklyn would: electroshock therapy
... he underwent electroshock treatment as a teenager to curb “homosexual tendencies,” an experience he described scathingly in his 1974 song “Kill Your Sons.”The lyrics to "Kill Your Sons" do evidently refer to the ECT, but there's not a word about the reason for it. Whatever the source for the claim, it doesn't appear to be Reed himself. So until we have a real source for it ...
The same goes for the claim that Reed "was widely rumored to have slept with both men and trans women in his Warhol years." That comes from Queerty, a site I trust about as much I trust Breitbart. (That Reed had a relationship with a "trans woman" is true, and I'll come back to that in a moment.) In any case, "widely rumored" tells us nothing about Reed, though it tells a lot about those who invented, spread, and believed the rumors.
I found one halfway good article on the matter, by Mark Joseph Stern at Slate, who concludes that although Reed was often referred to as bisexual, including by his biographers, "during his lifetime, Reed was perpetually evasive on the topic of his own sexuality." I haven't found anything yet that refutes that. The answer to the question "Was Lou Reed the First Openly Bisexual Rock Star?", then, would appear to be "No."
There doesn't, on the other hand, seem to be any doubt about Reed's three-year relationship with a "trans woman," though remember that "trans woman" is a twenty-first century construction that didn't exist in the 1970s, and since very little is known about "Rachel" we don't know how she identified herself. According to Steyn, Reed referred to Rachel as both "he" and "she," switching pronouns in rapid succession: "Nothing could impress her. He’d hardly heard my music and didn’t like it all that much when he did." Rachel inspired a notably phobic reaction in Lester Bangs, who described her in terms that fit his background as a Christian cultist but not his pose as a sophisticated rock critic. But the Sixties and Seventies really weren't as cool as people would have you believe anyway. Depending on how you define "bisexual," then, it may be that Reed was bisexual without being openly so, while the openly (because declared) bisexual David Bowie wasn't really bisexual.
The rumors about Reed's sexual orientation also tell a lot about attitudes toward and beliefs about sexual and gender nonconformity in the Sixties down to the present. Steyn, for example, writes:
During his glam rock years, Reed’s on-stage persona frequently bordered on androgyny, which—combined with his well-known and tumultuous friendship with the openly bisexual David Bowie—created an impression of epicene pansexuality.Steyn is critical of writers who carelessly throw around the word "bisexuality," but he's just as careless here. What does he mean by "bordered on androgyny" and "pansexuality," "epicene" or otherwise? I've quoted before Ellen Willis's confused take on such words: "Androgynousness is an important part of what the Beatles and the Stones represent; once upon a time Mick Jagger's bisexual mannerisms and innuendos were considered far out." They still are, since a mildly sissy young man with a high-pitched voice like Shamir Bailey still unnerves many critics and journalists. (Katha Pollitt pointed out during the Monica Lewinsky scandal that American journalists, despite their pretense of sophistication and worldliness, are very conservative about sex and gender.) As Reed told Lester Bangs in an interview Steyn quotes, "Guys walking around in makeup is just fun. Why shouldn't men be able to put on makeup and have fun like women have?" Exactly. It's fun, if you get into it, but it's not specifically gay. In a part of the same interview that stuck in my mind (I read it when it was first published) but that Steyn doesn't quote, Reed also said:
"The makeup thing is just a style thing now, like platform shoes. If people have homosexuality in them, it won't necessarily involve makeup in the first place. You can't fake being gay, because being gay means you're going to have to suck cock, or get fucked. I think there's a very basic thing in a guy if he's straight where he's just going to say no: 'I'll act gay, I'll do this and I'll do that, but I can't do that.' Just like a gay person if they wanted to act straight and everything, but if you said, 'Okay, go ahead, go to bed with a girl,' they're going to have to get an erection first, and they can't do that."I saw this interview in the Detroit-based rock magazine Creem, which at around the same time published a think piece on homosexuality in rock. I must see if I can find it. I remember that it referred to Iggy Pop as a "blatantly bisexual rocker" ("bisexual" again!), but I've never seen anything to back that up. (The picture of Pop dressed in a slinky dress and carrying a purse, again, does not tell me anything about who he has sex with.) Speculation, gossip, rumor are fun, but they're not reliable information.
And this, for example --
The weird sex part of his public persona was there from the very beginning, in the Velvet Underground's name. It was taken from a 1960s book about America's underground S&M scene. If that reference wasn't enough of a hint, there's the song "Venus in Furs" on the Velvet's first album, an homage to the erotic novel by the man who gave us the term "masochism."-- although it was written in 2013, has the same OMG-giggly adolescent excitement about even mentioning "weird sex" that I might have expected from a thirteen-year-old in 1967, but not from a presumable adult four decades later. Ditto for Queerty's take on "Venus in Furs." I get the impression that none of these writers remember or have bothered to inform themselves about the anti-censorship struggles of that period. Reed and the Velvets were riding a wave, not going anywhere new themselves.
I consider it a good thing that Reed wrote about sexual variation and kink, along with the other taboo subjects he took on. I never felt personally addressed by it, though, because 1) aside from liking boys I was really not all that far out, and 2) even as a teenager I could tell that Reed and the Velvets were deliberately trying to shock, but since I'd already read a lot of the literature they referred to, I knew it was old hat, dating back centuries. Most of my peers, of course, didn't know that, and even fifty years later, people still don't know much better.
* I'm using "queer" in its broadest sense here.