All throughout life, people have different groups of "friends."
Adults or children.
There are neighborhood associations, school friends, relatives, sport group friends, etc.
You cannot, invite ALL of these people to every party your child has.
Would you invite, the Adults of these groups, to ALL of your own parties?
No.
And so what if the neighborhood knows or sees you have a party.
At home.
Just because you or your kids associate... with various groups or people, it does not mean you have to invite them to EVERY occasion, that you have.
And not everyone, IS, a "friend" or "best friend."
Per my kids, we invite who my kids wants to invite. They are 6 and 10 now.
We invite, THEIR friends. We set a number of kids we can invite, tell our kids, then they and we make a list. And also per budget.
We do NOT invite the neighborhood kids.
We each have our own, lives. Even if the kids know each other.
And certainly, if some kids are just icky and awful... me AND my kids, steer clear of them and we do NOT let them in our house.
It is our, house.
Our own life.
Our own privacy.
Our home is not a mall.
Personally, I would NOT invite any neighborhood kids. Because if you invite just one of them, then, that will get sticky... and then the "neighborhood" will wonder why you didn't invite the other neighborhood kids or their parents.
Keep this to a "school classmate" party type thing.
Being "neighborly" does not mean... that you have to have the neighborhood kids over all the time, anytime, anytime THEY want to be IN your house especially if they rudely invite themselves over, nor letting the neighborly thing affect your every move in your own personal and private life.
If you overly harp on "how the other kids will feel if they are not invited...." then gee, what a burden on your child's shoulders.
How old is your child?
When my kids have b-day parties, they only invite their friends. NOT the whole classroom etc. and then they are discreet about it and do not go around blabbing or bragging about it in front of the other kids who are not invited.
If you are always....going to be concerned about what the neighbors think... then, re-think the B-Day party and have it not in your home.
But someplace else.
Then the other lesson in this is:
Teaching your child about how to choose friends.
Meaning, you do not have to invite those 2 "icky" neighborhood girls over. You do not have to, continue or nurture... a "friendship" with them.
I certainly would not invite kids over nor let them in my home, if they were not my cup of tea. My kids, also would NOT want kids like that in our home, nor would they want to play with them, nor would they want to be... "friends" with them.
Just because there are kids in your neighborhood... it does not automatically mean... that you are all BFF's nor that you have to let them come over especially if they are NOT nice to your own child.