Essentially, the core disagreement is about what is or isn't white supremacy. There isn't one way to define this, but if you start asking for things like "disavow white supremacy!" in a conversation like this then you're essentially just chucking good faith out the window. The context here matters a lot.
I wouldn't have "denounced" white supremacy either. If these are the base conditions under which you're prepared to talk to me then quite frankly, fuck you. There is nothing to gain for me, and you're clearly not prepared to take anything I say in good faith. Okay, I might have in a leadership role to keep the peace as a matter of professionalism, but I'd also have started looking for a new job as this is not a healthy atmosphere. I don't want to work with people who think I'm secretly a white supremacist.
The problem is that I've seen many things being labelled as "white supremacy" that seem ... a bit of a stretch. For example people have argued that Alien (the film) is an example of white supremacy as the alien represents a stereotypical black women; "Black women have been portrayed in contemporary white social and political culture as super-fertile and indestructible breeders whose sexual reproduction must be controlled."[1]
When I first read that, it took me quite a while to realize this was even referring to the alien itself, rather than some character that got infected. It seems it purely based on the fact that the alien is black.
There are many, many examples of this, especially in the last year people have been going way to far in re-analysing everything through the lens of race, often with some very harsh words like "white supremacy". Sometimes this is a good thing, but often I find it's not. Either these are general problems that affect everyone (just black folks more, but that doesn't mean the core problem is racism), or it's outright nonsense like the above.
Now, I don't know what argument that person made exactly in support of "White supremacy existing at Basecamp", but if you make such a strong claim – which is essentially calling your leadership/coworkers white supremacists – then you better have some good arguments. I'm skeptical they existed; they're certainly not present in this article beyond wishy-washy "creating a space where people do not feel welcome".
And considering that this discussion left people "crying and screaming at the screen" it seems rather easy to make some people feel "not welcome".
The entire thing stinks; perhaps the leadership could have handled things a bit better here and there, but if you're not willing to take a somewhat nuanced disagreement in good faith then there's nothing you can do except nod and smile on every sort of nonsense they bring up, and anything else will upset people.
[1]: https://theconversation.com/how-hollywoods-alien-and-predato...