Here, I will forward what I believe is a more accurate framing: Some people are single-issue activists that are only concerned about a single form of marginalization, usually one that impacts them personally. Single-issue perspectives create a distorted view of the world, and lead activists to propose solutions that will help some people while hurting others and leaving countless more behind.
This is a major problem in the atheist and secular movements. What we see as a result of this is the left ceding ground to the alt-right in these arenas, resulting in the further exacerbation of what were already heightened challenges imposed on secular people of color when it comes to finding communities and accessing resources.
If a critical mass of EC-centric leftists manage to successfully jettison IP activism from the movement, I can tell you what will happen. Prejudice will fester and, left unchecked, people will express it more and more, especially toward women and minorities. These latter groups will find such settings intolerable, and they will abandon them in the same way that radical feminists fled sexist leftist organizations in the 1960s, and how LGBTQ+ people eschewed socialist/communist groups in the 1990s.
This would be to the entire left’s detriment, so I entreat EC-centric leftists to reconsider their stance on IP activism.
What will happen is EC-centric leftism will never make any headway. The lessons go back further than the 1960s in the United States, all the way to the 1890s (and before), where racist rhetoric undermined the anti-trust (as in banking trusts) movement. What will happen is what continuously happens, which is that a plutocracy can pull this or that lever to eradicate solidarity by playing on the fears of a people mired in the politics of oppression. We need look no further than recent transphobic rhetoric to see concrete examples of how this works in practice.
Looking at it another way, we can ask that if fear of the other did not exist, would the GOP exist? Would anyone vote for such transparently odious people if they did not harbor tribalistic fears that could be manipulated? To say that classism is the foundation upon which all oppressions are built ignores how class structure is reinforced by racism and other oppressions. Elitist, greedy, warmongering politicians could not get elected if they could not appeal to these widely held fears.
So, yeah, you basically nailed it. If your leftism isn’t intersectional, it’s worthless.