Was the US Navy considered a gay haven before the Village People song?

This impression seemed to have grown in response to the Newport sex scandal, in which the Navy conducted a sting on male sailors going on land to have sex with other homosexual men. The trial received plenty of public attention (even greatly embarrassing Roosevelt--then Assistant Secretary of the Navy--due to the tactics he employed and the criticism of them in the media). It certainly contributed to the image of predatory gays as the first of the "lavender scares", so it wouldn't surprise me if it also created an image of the US Navy as a gay haven.

Later on, homosexuality was proclaimed by Philip Wylie in the enormously popular Generation of Vipers (1945) as being "...common in the Navy". Also in 1945, four thousand homosexuals were let go from the Navy under Section 8 and placed in mental institutions. It's not unlikely that these two events were linked.

At this point, discussions of the US Navy and homosexuality (though other Navies certainly carry on) largely stop. It's not until the 60s that Tom of Finland begins to draw sailors in lewd positions (though even this wasn't the US Navy, just loved by gay men in the US), and it takes until '77 (two years before the Village People song) for the first mainstream, fictional depiction of homosexuality in the Navy: the Jeffersons episode, 'Once a Friend'--though even that doesn't depict the US Navy as a "gay haven".

Essentially: yes, for about two decades. After that, not really.