The point of confusion seems to be what "tax exempt" means.
It means that you do not pay tax on items you purchase. You still have to
collect taxes on items you sell, subject to state and local laws on sales
tax. If admission to other events is taxed in your state, city, or
county you would be expected to collect and pay that tax on admissions to
the museum. You may have a tax exempt number through your parent
organization or you may have an individual number depending upon your
administration.