My BP is typically 90/60 or even 80/55 and I am perfectly able to donate blood.

It depends on why the BP is low and what symptoms the person experiences when it rises or drops. On paper and without context, you have hypotension; 90/60 is the textbook top end for hypotension, actually! (At least it was in my A&P and nursing textbooks, and in my clinicals.) I would absolutely be concerned if I saw that while taking your BP, and I'd ask for more info. Of course there are some people (older, very low body weight, etc) for whom that range is normal. You said you've donated blood in the past and been fine, so for you donation with what looks like a low BP is not a problem because barring some sort of medication condition or medication that causes your blood pressure to be in that range, that's normal for you.

OOP gets dizzy and faints when they donate blood. Their systolic is fine, diastolic is on the low end of normal, but that they get dizzy and faint is not normal, and absolutely is cause for concern. I've worked blood drives; if someone comes in and I see 105/65 and they tell me they have a history of dizziness and fainting after donation, I'm definitely concerned.

Given that she experiences negative health effects -- fleeting or not; fainting is not a trivial experience - puts her out of AH territory for me.