Tabitha,
More women attending climate change rallies and more women speaking truth to power does not mean women care more about Climate Change. Yours is an observation that women are doing more in this arena.
We are dwelling in gender stereotypes, big time. So with apologies, here goes. If men are the primary wage earners of households, then they can not risk not bringing home the bacon by attending demonstrations or raising their voices for social justice. (If women are marginalized then they have nothing to loose and will not have access to decision-makers to just talk.)
Our stereotypes are linked to our language. Consider the difference we assume between maternal and paternal. Maternal is nurturing caregiving. Paternal is providing for and protecting. Thus, worried for survival of polar bears is more maternal and worried about the impacts on family of an oil spill is more paternal. One is not better than the other. Attempting to keep score is futile. It is only striving for justice together that we succeed.