Amid growing tensions over the Ukraine crisis, some in eastern Europe have blasted Wurst as an example of the West's decadence. Activists in Belarus have even urged the country's state television network to edit the Austrian entry out of its Eurovision broadcast.
Russian legislator Vitaly Milonov accused the Austrian performer of "blatant propaganda of homosexuality and spiritual decay."
"I can only say 'Thank you for your attention!' If this is only about me and my person, I can live with it,'" Wurst said about her critics in emails Wednesday with The Associated Press.
"You know, I have a very thick skin. It's just strange that a little facial hair causes that much excitement. I also have to add that 80 percent of the autograph requests that I get are from Russia and eastern Europe — and that's what is important to me," she said.
Lisanne Wilken, an anthropologist at Aarhus University in Denmark, said the criticism against Wurst would have been trivial if it weren't for the Russian law last year prohibiting so-called gay "propaganda."
She noted there's been a lot of "transsexuals, transvestites and drags" in the Eurovision Song Contest, including Israel's 1998 winner Dana International, who had male-to-female gender reassignment surgery several years before competing.
The European Broadcasting Union, which organizes the event, has not received any formal complaints from the participating broadcasters, spokesman Jarmo Siim said. A national broadcaster is not allowed to edit out the live coverage, according to the EBU.
Neuwirth, who was born in Gmunden, central Austria, entered show business eight years ago, taking part in an Austrian TV talent show. After joining a boy band that quickly broke up, Neuwirth first appeared as Wurst in another Austrian talent show in 2011. She also took part in two reality shows, including one where candidates had to survive in the Namibian desert together with native tribes.
As she prepared for her performance in Copenhagen, Wurst said she wasn't paying much attention to the controversy about her.
"Hey, I'm just a singer in a fabulous dress, with great hair and a beard," Wurst told AP.
The annual competition is supposed to be completely removed from politics. Neither Russia's entry — teenage twins Anastasia and Maria Tolmachevy — nor Ukraine's Mariya Yaremchuk, whose routine includes a dancer running in a giant hamster wheel, allude to the recent tensions between Moscow and Kiev.
However, the Ukraine crisis has raised anew questions about the competition's scoring, which is partly done by phone voting across Europe.
Even though Russia has annexed Crimea, votes from the Black Sea peninsula will count for Ukraine because the phone operator there is still Ukrainian, the EBU said.
At Tuesday's semifinal, the audience booed when it was announced that the Tolmachevy twins had qualified for Saturday's final but cheered when Yaremchuk got into it too.
Both have "become the human face of the conflict," Wilken said, noting Ukraine seems to be some receiving sympathy support.