Attributes for Project and Program are shared, there isn't technically an Object called Program. There is only an object Project, where there are Program views.
Thus, an Attribute marked as 'Value Required' is automatically shown in Project Create and Program Create views.
A suggestion, untick the 'Value Required' on the Project Attribute. You can then remove this attribute from the Program Create view. From the View's Fields in 'Project Properties', make the attribute as 'Value Required. The attribute won't show in the Program views, but will still be mandatory for Projects.
I am assuming this is a custom attribute, where you have the ability to modify 'Value Required' for this attribute.