Not to get totally off topic but in the US, the York princesses are really not well known. Not in the context of William and Harry, who are known for being Diana and Charles (moreso Diana's) sons. Covers of Diana sold very well in the States.
We know that Sarah and Andrew had two daughters, but still I wouldn't think anyone could pick them out in the crowd. The same could be said for William and Harry but they have a little more face and name recognition.
From what I can see, those in the US who know of Andrew respect the fact that he is a veteran. Especially since for all intents and purposes, it appears that people of mean sometimes have a tendency not to serve. Not all mind you but a few names come to mind. Veterans are very revered here (as they should be). As they are revered in other countries as well.
Americans (for the most part) who like Sarah like the fact that she is a survivor. She has a plucky sense of humor (can laugh at herself) and is very comfortable with herself (faults and all). It should also be noted that on the whole her selling herself (and using her royal connections) are not really frowned on. Its not what you know but who you know. Sarah, Duchess of York is legally her name. She had a debt, she cleared it up (it appears both times). Why hate?
It should also be noted that at present both Andrew and Sarah don't get a lot of press in the States. So a lot of people here (other than us royal watchers) are not aware of the controvery that surrounds Andrew and his travels. Sarah is pretty low key here, other than than Hello Magazine and probably the NY Post, there wasn't much of a mention in the press of her recent financial issues. She is not a corporate sponsor of Weight Watchers anymore so we barely see her on television, in print, or on the telly.
Finally, this is all my personal opinion of couse so I am sure others will disagree.
ETA: I would also agree with Odette's comments regarding the British accent. We love a British accent. And honestly, we love the British monarchy as well. As long as it isn't ours
As previously mentioned in other threads, when other foreign royals visitthe US it doesn't get much press unless it happens in the city that they are visiting (Maxima and Wilem in NYC, Mary and Frederick in Chicago, and Felipe and Letizia in NM). I live in the Washington, DC area and if it wasn't for this forum or the internet, I would have never known that they were in the States.