Cook said in a magazine editorial he hopes his example will inspire others to push for change.
In socially conservative Alabama, where gay marriage remains illegal and workers can lawfully be fired on the basis of their sexual orientation, some said they wish the Apple executive had kept his sexual orientation private.
Charles Murphy, mayor of Robertsdale, the Gulf Coast city of about 6,000 where Cook spent much of his childhood, said he is proud of Cook's achievements in the business world but would have preferred not to hear about his private affairs.
"Tim has done a good job with Apple. We're very proud of the accomplishments that he's made," said Murphy, who ran without party affiliation. "Sometimes people's personal lives need to stay personal."
When inducted on Monday into the Alabama Academy of Honor, Cook made comments critical of the state's progress on rights for gays and minorities.
Alabama Governor Robert Bentley, a Republican and opponent of same-sex marriage, said afterward that he objected to connections Cook drew in his induction speech between the civil rights movement and gay rights, the Anniston Star newspaper reported.
"I don't connect those two, and in fact I don't think the African-American community connects those two either," Bentley said, according to the newspaper.
Bentley's office did not immediately respond to messages seeking comment.
Others contacted by Reuters, including church employees in Robertsdale and computer repair workers near Birmingham, declined to comment on Cook's announcement.
(Also see: Tim Cook Says He's Gay: Zuckerberg, Nadella, Pichai, Clinton, and Other Reactions)
Birmingham-based state Representative Patricia Todd, a Democrat who is Alabama's sole openly gay lawmaker, said she drew strength from Cook's announcement, made in an article he wrote in Bloomberg Businessweek.
Todd said the prospects for a bill she plans to reintroduce next year to legalize gay marriage will be strengthened by Cook's example.
"I'm tickled to death," Todd said. "He is saying what we've been saying all along. Equality is good for business."
Not everyone reacted strongly to the news of Cook publicly proclaiming his sexuality. Delaney, a worker at a Robertsdale church who declined to give her last name, said she had never heard of Cook, and had no comment on his announcement.
"I'm just impressed that someone from a town as small as Robertsdale is the CEO of Apple," she said.
© Thomson Reuters 2014
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