In the country where I live, the USA, men comprise the vast majority of legislators (those who make the law) and the judiciary (those who interpret and enforce the law). As a result, men are largely in control of birth control policy, educational policy, family law, etc. Women do not have a lot of practical or real power on these issues.
As for feminists, just who exactly are you envisioning that they need to work with? Men? You know, feminism isn't exclusive to women - lots of men are feminists and work on feminist issues as well. And gay groups, who do they need to be working with? Straight people? The vast, vast majority of people working to secure LGBT rights and organizing around LGBT issues in my country are straight. I'm not exactly sure what these imagined groups working in isolation and in opposition to the rest of the population you think are, but you don't seem to be very well informed on what actual feminists, activists etc are or do.
I think that depends. If your company has, say, a reputation for making games that degrade women or throws holiday parties that feature hired topless women, you're sending a message that will turn off a lot of potential female applicants. If a company isn't getting a lot of female applicants for their positions, I think at they very least they do need to consider (to an extent) how their corporate image or recruiting policies might be playing a role in shaping their applicant pool.
EDIT:
From the article:
From the first page: