Healthcare staff in A&E will prioritise patients based on their immediate need. If you're having breathing difficulties (and apparently, Phillips' lips were turning blue, so that's quite serious), you'll be treated quicker because it's more urgent.
This makes it sound like there's some kind of sectarianism in our healthcare, and is frankly a stupid thing for an MP to say. But Jess Phillips has never been the brightest.
While you're generally right about triage, it's absolutely believable that she could have been prioritised by Palestinian staff over patients with a similar level of urgency, in spite of them waiting longer. However she definitely shouldn't go around saying that - it reflects badly on the staff.
Edit to add, on a more serious note: If I was an NHS employee I'd be absolutely outraged at the implication that the quality of treatment they provide is dictated in any part at all by the patients' political views, rather than by the (lack of) budget, training, and available staff, which Labour is complicit in.
Seriously, the more I think about it, the more annoyed this bullshit is making me.
That's far more likely. Although hospital staff aren't supposed to prioritise celebrities, I think they have some leeway if they believe having them sitting the waiting room will cause security or other issues.