I should clarify a distinction between two types of identity politics: one is focused on dealing with overt and egregious oppression and one is focused on generally improving the role of and removing roadblocks for an identity group. The latter are really what this article is about, but in cases such as the civil rights movement in the mid-20th century US or the gay rights movement of the 1960s-80s, where there really isn't enough social equity to even open a dialogue, most of what I say toward the end of this article may not apply, or may apply in different ways.
Back to Freemasonry...There are two obvious answers to the question: what does Freemasonry have to contribute in this realm? I believe that they are both wrong, but because they're such widely made arguments, at least in my own experience, I'm going to tackle them first and then move on to why they are wrong and what I think Freemasonry brings to the table.
NothingBecause Freemasonry (at least as practiced in what most of the world considers "mainstream, recognized jurisdictions") explicitly disclaims any role in the political sphere proper, it is an obvious and, perhaps not entirely unjustified claim that we have no role in identity politics. We don't discuss politics in open Lodge; we don't use Freemasonry as a platform for our political advocacy; and our administrative apparatus (the Grand Lodges) are not politically active outside of their own internal structures.
We have always been hereFreemasonry, of course, has been what some have thought of as a nexus of identity politics for over 300 years! We're an all-men's organization (with some notable exceptions around "adoptive" rites and youth groups that are satellites of the main body of Freemasonry) and we have a strict requirement of a belief in a supreme being. We're arguably the oldest identity-oriented social structure in the West outside of religion (and perhaps some ethnicity groups in Europe). So it might seem obvious that we're not just able to contribute to, but are at the heart of the notion of identity politics.
Our Actual RoleBut these are both misleading and ultimately untrue, though to different degrees. It's true that Freemasonry has no explicit role in the public political sphere, and this immediately tears down the second claim. But the first claim is only a part of the story.
Freemasonry has always had something to say about the translation of abstract philosophical ideas into the public sphere, through the transformation of the individual, and in this sense, it can speak to the dangers of identity politics and to the importance of identity perspectives.
First, let's talk about the dangers. Politics has a rough equivalent of the second law of thermodynamics: for every action there is an equal and opposite reaction. But the political equivalent is more nuanced. For every political position that is advanced in society, an opposing political position is empowered. This does not speak to equalities the way physics can, and that's because the thermodynamic-like properties of politics tend to be quite complex, and the A=B sort of equalities are quickly lost in diffusion through many competing perspectives.
We do know, however, that political movements empower those who are inclined to disagree with their aims (as might seem obvious). This means that creating an identity-focused political movement tends push fringes that oppose that view further into the mainstream. So, when women, for example, advance deeply women-focused political ideas such as feminist epistemology, fringe men's rights groups that were otherwise not taken seriously by the mainstream right begin to advance into the light of day.
But Freemasons have long known that a shared group identity can give an organization a profound capacity to give its participants new perspective on their situation. The reactive men's groups that form in response to feminism, for example, are not going to be focused on improving their capacity to support women's needs in society to equality and dignity, but as a group that affirms the value of the individual, Freemasonry can inspire men to contribute in those areas (as much more eloquently put by Wor. David Riley), thus improving both their own situation and that of women.
What we have to contribute to modern identity politics is a 300+ year old perspective on what works and what doesn't in seeking to improve society by improving the capacity of the individual to reflect on their role in that broader context, and any identity group that takes on that, much more complex and difficult challenge is going to find that the inherent resistance created by advancing agendas based solely on an identity do not go away entirely, but they are substantially reduced.
In short, what Freemasonry has to contribute to identity politics is a way of accomplishing the same goals, within the same groups, but without having to be oppositional. As a men's group Freemasonry does not need to oppose women and women's rights, nor do individual Freemasons. As a faith-oriented group, Freemasonry does not have to oppose atheists, nor do individual Freemasons. And as a continuance of Western ideals, Freemasonry does not have to oppose the vastly expanded interactions in our modern society between East and West, and indeed, many Freemasons have helped to enhance the value of those interactions.