Back when I was in USAF Basic Training (1960s), we were given a special briefing, and we were told that any of us were "that way" and wanted to say so, we would be sent home and returned to civilian life.
The officer explained to us that the reason this path was offered was that homosexuals were a security risk. (The reason was repeated several times.) Nothing about offending anyone, only that homosexuals are a security risk.
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Same speech I heard over and over and over for 16 weeks.
Arlo Guthrie alludes to this in his 1967 anti-draft song, “Alice’s Restaurant.” He says something to the effect that if two guys together, at their draft physical, sing “You can get anything you want at Alice’s restaurant,” that “they’ll think you are both faggots and won’t take either of you.”