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Excellent point.
I see several problems:
1) We would have the situation that the Catholic church now faces. It’s seminaries are so infiltrated by gays that heterosexuals are avoiding them.
2) Gays would promote gays, making it difficult for hetersexuals to make a career in the services. This would discourage hetersexuals from joining.
3) Our armed forces would become ever more liberal in political orientation. Personally, I would use the word Marxist. We could no longer count on Constitution loyal officers willing to remove a Chavez-style president.
Source?