I struggle with the term men's rights activist. To many it means a traditional conservative who opposes gender equality. In my experience, there are many men embrace gender equality and are discontent that society seems to only be concerned with inequality of genders with regards to women's rights (gynocentrism).
Like you have said in this article, as women gain agency, they should lose the privileges that accompany not having agency. Women have gained enough equality to declare they don't need men anymore, which they frequently do online. I read that study that you referenced and indeed the Index score hasn't changed much over the last 5 years. However, I bet if they showed the change over the last 20, it would be astounding. Little has changed on the other side of the equation with regards to criminal sentencing (trying to stay on topic).
Ideally we should either be more lenient on men or harsher on women (one or the other) to address the imbalance. However, this isn't happening and Feminists aren't going to push for it. I don't believe that this will change automatically. I think MRAs (and anyone for that matter) make a fair point when they point out this disparity.