Most white collar (and some blue collar, as noted above) businesses are closed the entire first week of July. The number of businesses normally open on July 3, but closed this year in observance of the Holiday, will be very small -- and comprised mostly of small businesses (like that 3 person State Farm office you deliver to). That's especially true with more retail increasingly open 364 days (and in some instances ,365) days a year.
Don't know about you, but on my route, I had 60 business and 40 residential. Of those 60 business, 55 were the small 3 person State Farm type offices you are referring to.
Yes, the retail will be open. But close to 3/4 of our business stops, not packages, are the small State Farm, Dr's office, tool shop, etc.
I still say 1/2 to 3/4 of the businesses will be closed. The businesses that are normally opened Saturday may work Friday and take Saturday for the holiday, but this is very few.
Government is closed, banks are closed, schools are closed, we'll see as the closures come in.