The projection for a geodatabase cannot be changed by design; this prevents making changes to the feature dataset which maintains these settings for the feature classes it contains. When using the schema wizard to create a geodatabase from a repository, the spatial reference needs to be set. This includes setting the geographic or projected coordinate system and optionally specifying the spatial extent, M domain, and Z domain for all feature classes within the dataset.
As a workaround, run through the schema wizard in ArcCatalog to create a new personal geodatabase, and set the spatial reference when creating the feature dataset. Then, data can be successfully loaded into the geodatabase as long as it is within the defined extent.