I thought what Hannah said was totally reasonable tbh. She wasn't calling anybody a racist, and she made a point of saying she wasn't putting it on Rebecca, she was just explaining how it makes her feel to be labelled as aggressive, and her skin colour (and stereotypes) is a part of why it makes her feel that way (and this thread alone has posts that show she's justified in feeling that way)... so there simply wouldn't have been a way for her to explain her feelings
without mentioning race (and isn't explaining your feelings just a normal way of resolving an argument). It would have been different if she was saying 'you're calling me aggressive
because I'm black' but that's not what she was getting at at all. There is a stereotype of the angry black person whether people acknowledge skin colour or not, and the answer of 'she shouldn't show aggression then' is no good because she shouldn't have to be held to different standards because of a stereotype that's imposed on her. Sometimes people are aggressive, black or white, but yes black people tend to be more harshly judged for it and it's the unfairness of that which caused Hannah to bring it up.
I don't think it's 'playing a race card' just because someone mentions race, especially when there's context to it and they've got a point to what they're saying. I actually think that some people just hear race being mentioned and jump straight to the race card card (it's a thing

) without thinking about why it's brought up in the first place (again, she wasn't being accusatory so it wasn't about trying to call anyone a racist). If anything it was probably quite brave of her to mention it because she's probably aware enough to know the race card accusations would follow.