Awards in which gender identity is a requirement
I applaud your friend for refusal to participate on ethical grounds. I think your second question can be answered in the negative. But not making a public statement leaves the (unfortunate) status quo intact. 

The first question however is, at this time, pretty opinion based and some research might actually help settle the question. It isn't my field, so it is possible that something has been researched and reported. 

But we are in a time of change. The past was bad. We hope the future will be better. But there is still observable discrimination against women and many others, especially gender fluid individuals. Hopefully this will sort itself out if enough people get enlightened. But there are observable disparities in treatment even when it is (largely) unintended. And those things won't just dissipate without pushback. Individuals of "good will" need to be part of the pushback even (especially) when they aren't part of people and groups who are discriminated against. 

But (opinion), if such awards tend to highlight the underlying problems, then they might be useful. And I hope that such things can go away in the future. A future in which individuals are judged only for their own accomplishments and not, at least in part, for things over which no one has any control. 

I believe that more than one Nobel Prize has been given to a male whose female student actually did the work and had the breakthrough. 

Fifty years ago, in the US, we thought, through the civil rights movement, that we were approaching a better future. Sadly progress has been slow, at best. Maybe stalled. 

The arc of the moral universe is long, but it bends toward justice. (Attributed to several people, including Dr. Martin Luther King, Jr.)