Take underrepresented minorities in tech (presuming yours is a tech workplace): You can work on that in a "nonpolitical" way. (It is, as you say, still politics, in a way, but it's not being done like it's politics.) You say, "You know that Android developer position that's been open for four months, that we can't find anyone for? I wonder if there might be some non-traditional candidates that would fit that role. How could we go about finding them?" That's done in a non-political way. The emphasis is on "this could help the organization".

Or, you could address the same issue by saying "We need to pressure HR to require them to present at least one under-represented minority candidate for each open position." That's a much more political approach to the same problem.

On a more general level:

> We can’t improve without discussion, and it’s unfortunate that these type of issues are so divisive.

Sure. But don't do the discussing at work. That's not what work is for. (The exception is when the problem does affect work. If the workplace is trans-hostile, say, you need to address that at work, and there's probably not a non-political way to do it.)