Can I alter a view being referenced with schemabinding if the change fulfills the binding requirement?
You don't need to drop the dependent views, but you do need to alter them to (temporarily) not be schemabinding. If any of them are indexed, this means you will need to re-create the indexes. 

SQL Server doesn't have some weighting system for schemabinding: you can't change the object. Period.

ALTER VIEW dbo.view_name
--Remove this WITH SCHEMABINDING
AS
  SELECT ...