No, it is no violation of non-profit standards for a
not-for-profit to charge admission, or multiple admissions. Non-profits are
not required to operate at a loss. They are allowed to make money although
it is very difficult for them to do so.
While you may be upset at the price, I am sure the $16
admission did not approach covering their cost of operating to support your
visit. It is stunning to calculate the cost of operating a museum on a per
visitor basis. A good book on this topic is "The Cost of Collecting" (hope
that title is right.) It came out about 10 years ago. At that time the
cost per visitor came out to about $30.