A.J.
Wow! You sure did receive some very interesting responses about this so I felt compelled to respond as I completely understand your position.
First things first, I am a teacher and I am a germ-a-phobe. I have had students with lice and recurring lice infestations. I have had lice from my students. In fact, I just opened a bag in August full of wool sweaters that were bound in plastic for past 8 years since I had had lice. As a teacher I know how sensitive parents are to lice. They do feel ashamed, embarrassed, helpless. I have listened to many upset parents regarding this. And it is very easy to figure out who in the class has it without the name ever being said allowed by an adult. Kids are pretty smart.
As a germ-a-phobe I completely understand you not wanting this girl at the party. I wouldn't either. Just as I would not allow a child at the party ho had a fever or had vomited in the past 24 hours or had a rash. Heck, even a runny nose and a cough send me into a tizzy.
Lice freaks me out. The person who has it does not freak me out. The lice freaks me out. I do not think it is an American cultural thing. I do not see it as a socioeconomic thing. Some people can tolerate these things while others cannot. I cannot.
I am happy you made a decision about the party and I am sure it will be a success. Don't let some of these harsh responses get you down. I understand you completely! Happy Birthday to your daughter!