Variant Creutzfeldt-Jakob disease (vCJD) - my parents lived in the UK for six months during the period 1980-1996. Can I donate?

Yes, as long as you didn't live in the UK for six months or more during that period. 
The variant Creutzfeldt-Jakob disease (vCJD or 'mad cow') deferral policy on UK residency applies only to residence after birth. It doesn't matter if your parents are excluded, or even if your mother was pregnant with you while living in the UK during this time.