Why is it important to choose a Family Bank that is accredited?
In some countries, national regulations hold Family Banks to the same standards as Public Banks, so an independent accreditation is not necessary (Examples: Germany, Israel). But in most countries the federal requirements for Family Banks are not as strict as Public Banks, and then a voluntary accreditation is desirable. For example, in the United States the FDA registers and inspects Family banks, but does not require them to have a BLA License like Public Banks.
Caveat: The process of registering with an accreditation agency and getting inspected can take a year, so it is understandable if a brand new lab does not have an accreditation yet.