As I've read "The Pink Swastika," Lively and Abrams don't allege that Hitler was gay, just the Nazis around him.
A German author alleges that Hitler himself was gay.
Dennis (Justin) Raimondo would be an example of what Lively writes about. Dennis Raimondo even gave the nominating speech for Pat Buchanan in California.
The OSS Psyche report on H indicates the belief that H was in fact a Homosexual, but couldn’t get DIRECT evidence. Only, discussions with “people in the know” that it was a known fact “in the community”
Some try to make the case against this by claiming H’s round up of Homosexuals for the death Camps was proof he wasn’t. The opposite was true. He rounded up the Homosexuals to silence them, pure and simple.