Doesn't sound like it was much of a secret:
[From
\"]http://www.whitecleats.org/gburke.html]Burke joined a Dodgers lineup boasting Lopes, Dusty Baker, Reggie Smith, Steve Garvey, and Ron Cey. During Burke's first full season with the Dodgers, 1977, the team won the division and played the Yankees in the World Series. Burke, who had played utility outfield and batted .254 in 169 at-bats, was furious that new manager Tommy Lasorda didn't play him after the first game. Burke had already manifested a dark side to his personality; he could be moody and sometimes violent, quick to anger and hard-headed. What began as a teasing relationship with Lasorda, filled with clowning around and practical jokes, eventually turned ugly on both sides.
Burke soon found a particularly effective way to get Lasorda's goat. He befriended Tommy's effeminate son, Tommy Jr., who would eventually die of AIDS in 1991. Rail-thin with wispy blond hair that fell over one eye like Veronica Lake's, Tommy Jr. was known in the gay world of Los Angeles as Tomasina. His straight nick-name was Spunky. Burke and Spunky became running buddies, frequenting the gay bars of Los Angeles. Lasorda, a Christian Bigot, was embarrassed by his gay son. As a practical joke, Burke and Spunky planned to show up at Lasorda's house for dinner in drag with their hair in pigtails but backed out at the last minute. "Tommy first would have shot us both in the head. Then he would have had a heart attack and died." Burke writes.
Such behavior was not designed to keep Burke's homosexuality a secret. Although he was initially well-liked as a rookie, new of his sexual orientation leaked through the organization, and his position within the franchise deteriorated. He would not keep his private and professional lives hermetically sealed from each other. While in the minors, he had revealed his homosexuality to Cleo Smith, another Dodger prospect who had grown up in the East Bay, and Smith had blabbed. Furthermore, Burke's visibility as a major league player exposed him to recognition in the gay community. Ric Williams, owner of an LA landscaping company, used to hang out at a gay bar called the Stud and became friends with Burke before realizing who he was. "I was watching a Dodger's game on TV, and Dusty Baker just hit a home run. The crowd was still cheering, and Tommy Lasorda let Glenn pinch hit, and he hit a home run right after Dusty. I said to my friend Scott, 'I know that guy! That's the guy from the bar!'" The next time Williams saw him at the Stud, Burke copped to who he was. "I try to keep it kind of quiet because they frown on any kind of homosexual activity," he told Williams. The Dodgers, during the late '70s, cultivated a company-team image, well-behaved and squeaky-clean.
Between the organization's gossip and Burke's own indiscretions, the secret was out. As Burke puts it bluntly, "They knew I was gay, and were worried about how the average father would feel about taking his son to a baseball game to see some fag shagging fly balls in center field." The Dodgers suggested he don the time-honored fig leaf for gay public figures. Vice President Al Campanis offered him a honeymoon bonus if he'd find a woman to marry. Burke refused. "How cruel would it have been to marry a girl while having no intentions of ever making love to her?" he demands in his autobiography. At the end of his second season, Burke found himself traded to the Oakland A's for outfielder Billy North. Suddenly his personal and public lives, which had been geographically separated, were brought into a proximity that sharpened the contradictions.