There is a non-profit organization operating in my neighborhood. This
home based non-profit relies solely on charitable contributions to pay
all bills.I am trying to determine if this non-profit is considered a
business. If so, it should be obeying local rules set in my town for a
home business.

Are they bothering you in some major way?  Perhaps it is best to let them be.

It would be helpful to know which town you're referring to. Or even
which country, as charity laws differ across the world.

I'm sorry.. the group is in Suffolk County, New York. The issue is
that there are clear laws for home occupation regarding keeping
traffic and annoyance to a minimum to protect the surrounding
community,  which is zoned residential in this case. If this were an
animal hospital or beauty parlour for example, it would be shut down
in a minute by the town. Since  it is a non-profit, the town seems to
have a problem defining it as a "business".

The home is run 100% by donations and staffed by volunteers.

Ken