Follow-up from "Remove unused public interface methods from GaudiCommon"

The following discussion from !1140 (merged) should be addressed:

• @cattanem started a discussion: (+1 comment)

  @clemenci could this MR be reverted please? Or, if you prefer, make the member variables m_typePrint, m_propsPrint and m_errorsPrint protected rather than private, otherwise derived classes cannot have consistent behaviour with the base class - see lhcb/Rec!2460 (merged) and lhcb/Phys!946 (merged)

To mitigate the incompatibility we should make the properties protected instead of private (which should be the norm).