> they are working (hard) to try to reduce those differences, at least in those ways that matter to a great many people.
Yes.
> It isn't the progressives that are highlighting and reinforcing differences
It is very easy to misunderstand or "misunderstand" a lot of progressive tools and messaging. Insisting on pronoun checks or insisting on defining someone's race as part of a drive for racial equality by necessity highlights differences. That can feel uncomfortable to anyone. It is easy to exploit that discomfort. I'm not asking for people to stop or minimize things like identifying their pronouns. That should be normal. But ... you can't insist on it. You can't force someone else to go along with it. They have to choose to participate.
Progress happens when individuals decide that it's worth their time and effort to push for equality. If the messaging pushes more people out instead of advancing equality, then the messaging is not good.
Most political messaging is more motivating to people who are already part of the movement (no matter what movement) than to outsiders. The Progressive movement by definition needs to motivate people who are not already aligned with a particular goal.