Jesus Christ the responses here!! I think if it were a FB group for a general group of women and the admin put up a picture of a group of only black women, plenty of white women could take that to mean "this is a group for black women", "is the admin trying to make a point by only including black women in the picture", "is this group not for me".
The OP doesn't seem to have addressed this by saying "hey, you racist bitches, how dare you". She simply pointed out that the picture wasn't inclusive. The women in the group took that to mean they were being accused of racism, and piled on, making it her issue instead of theirs. If they REALLY didn't want to be racist, they should have responded by saying "oh, I never thought about it like that. Sure, I'll change it, thank you for bringing it up" not "fuck you the white women represent everyone so the pic stays" 😂 How people think this is fine is beyond me. So, in short, no @UnshakenNeedsStirring you are not being unreasonable.
White people (I include myself in this) who really want to not be racist need to accept that actually, by the very fact that we exist in society, we have probably absorbed some of the institutional and structural racism that surrounds us. That's okay and it doesn't make us bad people, but we should be trying to reflect on how that may have affected our beliefs and behaviours on a subconscious level and then actively working to tackle those, rather than just shouting "I'M NOT A RACIST" any time anyone brings up a race issue. It mightn't be the most comfortable thing to face, but ignoring it won't make it not true 🤷🏻♀️