Europe didn't take the Monroe Doctrine very seriously, but with the Americans and British getting into a stalemate many believed this was the start of America becoming a world superpower.
men have jobs and responsibilities they might not be able to handle and they have limits in their responsibility and could be as liable to harm as much as women.
Wong-Woo was eventually allowed to enter because the Secretary of Labor overruled the denial. This suggests that Wong-Woo had a valid application for coming to the U.S.