For my campaign there is an option at higher levels to take a blood transfusion with a half orc half hobgoblin and I want the creature to take damage if they aren't either of those races, what damage type would that be?
Use rules for poison or disease
All possible damage types in 5e are:
The closest thing to the case you're describing is a disease. Diseases normally deal poison or necrotic damage. The precise amount depends on how severe this condition is, therefore, is totally up to you as the DM.
You can use poison rules for any suitable poison from DMG as inspiration. An example:
A creature subjected to this poison must make a DC 10 Constitution saving throw. On a failed save, it takes 6 (1d12) poison damage and is Poisoned for 24 hours.