Of course white women can be allies to BME women. The first (very America centric) article says as much - effectively some women responded as allies and some responded defensively.
Most activism is single issue. Black Lives Matter is most powerful as a message when it's about black lives, but when people dig down to the queer theory and anticapitalism they get confused or doubtful.
Feminism centers women. That's all it is really. Black women should be as centered as women of any other ethnicity, because your ethnicity is not relevant to whether or not you are a women, any more than your social class or income or whether or not you have children or your nationality or educational level or whether or not you have a disability has any bearing on whether or not you are a woman - it's just biology.
However obviously different women have widely different experiences - being black impacts lived experience in an all pervading way comparable to the way being female does. Being born with or aquiring a significant disability (a subject close to my heart) also impacts lived experience in an all pervading way, as much so as being female does IMO.
www.un.org/development/desa/disabilities/issues/women-and-girls-with-disabilities.html
"Women and girls with disabilities experience double discrimination, which places them at higher risk of gender-based violence, sexual abuse, neglect, maltreatment and exploitation. The global literacy rate is as low as one per cent for women with disabilities, according to a UNDP study"
Feminism should center all women. Sometimes unconcious bias means it centers non disabled middle class degree educated white women. That's not great. Some issues impact all women, and they shouldn't be dismissed as unimportant because they are not centering the right women.
There is a danger of everything being shot down by endless "whatabout"? "Why are you campaigning for better maternity provision in the UK generally and not focussing on the fact black women have the highest rates of maternal mortality in the UK?" it's a valid point, but should it mean the general campaign which doesn't mention race is bad? I don't think so, at all.
Everyone should listen to one another's experiences, and nobody should be dismissed, attacked, or told her experience is wrong.
That doesn't mean that women who enjoy white privelige aren't allowed to shout about the ways in which belonging to the sex class woman impacts them though. Just as rich black men can still talk about their own experiences of racism without being told to talk about poor black women's experiences of racism instead...
I think feminism centers women for being women first. That should mean all women, and the main issues are those related to being female. However we should listen to one another talk about how being black, or middle eastern, or asian, or regarded as "foreign", or poor, or disabled, or a mother, or gay, or a combination of those, have intersected with the core similarity of being female, and care about that.
That's what I think - internalised and institutional racism (as described in the second article posted in the OP) can coincide with feminism. That's a bad thing but it doesn't make feminism bad, it means that like every big, unfocussed, decentralised "movement" in vinverted commas it has problems which are hard to solve because it isn't a movement really, in the sense of having leadership and a structure or anyone in charge, let alone a company or political party or charity from which you can fire or expell anyone!
Your comment on posting "to let the record speak for itself" confuses me missyoumuch - do you mean you are gathering screenshot evidence for something?