Lots of things happened in apartheid, but the crux of it was that black people were segregated out and not allowed in certain white areas, which the whole world agrees is not right or fair. Which is why this not allowing white people in certain areas feels very similar.
Does it fuck. Similar? Seriously? There is one forum on mumsnet where you’ve been politely asked not to post unless you have experience of living as a black person and you think that’s ‘similar’ to being arrested for sitting in the wrong section or a bus, or being lynched for allegedly looking at a white woman the wrong way, or being forced to attend a segregated school where the resources and training were completely inadequate, or forced to use a separate entrance into businesses, or shot dead for protesting, or denied the right to vote?
You haven’t been banned from anywhere. You can bleat about it all you like, but it simply has not happened. Some black posters have simply expressed a view that they would prefer for white posters not to fill the board up with their opinions and experiences, since it’s about creating a community of people who specifically share the experience of being black.
You are no more banned from that board than you are from the LGBT board, but on both you should be refraining from sharing your views unless you actually have directly relevant experience. A black person saying to you that your opinions on racism aren’t relevant to them is NOT the same as you being banned. It’s just that you have nothing of value to add, so why not just move on?