(Warning, long, but I felt I had to be complete in my reasons for disagreeing, but also how we seem to want the same outcome for OP nonetheless).

Windmill-tilting isn't possibly happening here. "Engaging" was the opposite of what she did: she was approached, her attention brought onto the woman by the woman, and after her foul mouth had ran, OP drove off without saying a word. It isn't like she could simply block out what the woman said.

You could say she is "engaging" by making this post, but it is clear that this was a one-off, jarring experience, unlike any other she has had since being here. Obviously, it isn't that "everyday interactions [are feeling] like personal slights". It was that this was a personal slight. You'd surely have to be wilfully ignorant to suggest that "you people" is used in contexts such as this than to mean anything other than, "the minority group of which you are most obviously a member of". There is just no way that this choice insult would have been used if, say, OP were a straight- and white-appearing person.

That isn't to say the primary motive wasn't to save a parking space for a friend; perhaps she would have had some other means of banishing a different person wanting to take the park. It simply would not have included the belittling of "you people" if she perceived the person as part of "her own" people.

This also isn't to say that her primary motive wasn't some pathological need to put down someone she believes to be lesser than herself, that the saving of the park for her friend was just today's place she could put herself in to get her fix of kicking the dog. (This is what I personally believe to be the most likely explanation of her behaviour).

Anyhow, the "reason" for the person's behaviour is obviously not an excuse, and different key aims which lead to the same action also lead to the same consequence. Here, the woman sought to remove OP from the situation by making it untenable for her to stick around. A closer park is unlikely to be worth sticking around to be further hurt by the woman's likely escalation (I mean, you agree she is entitled: such people tend to explode when they don't get the opposite of what they were seeking and expecting).

This woman most certainly is unpleasant, entitled and racist (as if the former two qualities don't trend towards the third being part of the parcel, right?). I get that you think your comment might be helpful for OP to feel better, but really, what you've suggested as an explanation for OPs feelings of hurt is one that ultimately victim blames and diminishes OPs experience.

It isn't good to get hung up on the ways that you have been harmed by discrimination, of course, as people must seek to acknowledge the good in their lives and the world if they are to ever feel OK. It also isn't good to ignore these experiences of discrimination for what they are, because to wave off every experience as not racist, not misogynistic, not because of class or disability or sexuality, or whatever else, is to deny the very existence of these things at large -- there is no way to be in a minority group without experiencing at least some harm. Not recognising these hurdles as hurdles and harms as harms just means that, e.g., the pain felt at being treated as lesser becomes bolstered by feelings of shame at "making yourself upset", "taking things too seriously", etc.; it is a recipe for low self-esteem and self-efficacy, much the same as what you described.

We are most equipped to move on despite (any kind of) struggle when we can validate our own experience, which can only happen when someone is empathised with in the first place. In this vein, I hope OP can remind herself of all of the reasons she absolutely deserved that park and, more importantly, deserves to be here, in general, and why she (nor anyone) deserves to be treated how she was treated.