The patients, who would have died in infancy without the ops still suffer from health problems, and are now lodging a 700-name petition at the Scottish Parliament calling for better standards of care.
The move comes six years after guidelines to improve services were rolled out in England.
Gill Mitan, chairwoman of the Bravehearts patients' association, which represents adults with congenital heart defects, said: "Our concern is in the worst-case scenario that an adult presenting at accident and emergency will be sent home and suffer a cardiac death because they did not have timely specialist support."
It is estimated more than 15,000 adults live with congenital heart disease in Scotland. More than 3000 are thought to need regular treatment.
There is a specialist service for them at the Scottish Adult Congenital Cardiac Service at Clydebank's Golden Jubilee National Hospital.
Bravehearts praise the unit, but say there is no 24-hour access to it, and patients are often cared for by general hospitals.
Some put on monitors in A&E departments have said they were told the monitor must be faulty because "their heart should not be behaving like that".
Sandra Aitken, 34, from Kirkintilloch, said: "Every time I speak to a GP I have to describe my condition, because they do not have a clue. You can see them reading up on it."
Dr Hamish Walker, director of the Scottish Adult Congenital Cardiac Service, said: "We are committed to deliver appropriate care at all levels of the NHS for this group of patients."
A Scottish Government spokeswoman said work on looking at national services compliance against English standards had been deferred until revised English standards are available.