score:6
My girlfriend got in contact with her brother in Vietnam, who has a close friend that works at Tan Son Nhat International Airport. Long story short, this will not be a problem entering the country.
Ultimately it seems like it's up to each consulate to put information in the MRZ field or not.
UPDATE:
After entering Vietnam successfully, I can officially say that it's up to each specific consulate to decide to use the MRZ or not. It did not cause any problems when entering the country.