The Adopted People's Association (APA) is furious the situation will force people to deal with the country's adoption agencies, instead of accessing records independently.
"Our members have complained time and time again about the lack of help, understanding and respect from these agencies," said APA chairman Anton Sweeney.
Under the existing paper-file system, available to the public since 1859, an adopted person can begin a search with just his or her birth date. The APA said the computerised system needed, at a minimum, the mother or child's surname and a date of birth.
"Obviously, the vast majority of adopted people would not know either of these names and, therefore, in future will be unable to find their birth certificate by themselves," said Mr Sweeney.
The APA said the natural mothers of many of their members, some of whom were subjected to clerical sex abuse, were victims of both the Church-controlled Magdalene Laundry and Mother and Baby Home systems. Many cared for their babies for up to two years, until State payments to the institution ran out. Their babies were then placed for adoption, the institutions receiving generous donations in many cases. Mr Sweeney said many of the babies were also used as guinea pigs in drug trials without the knowledge or consent of their natural mothers, before being placed for adoption. These trials are under investigation by the Laffoy Commission.
Last night in Dublin, the APA held a meeting urging adopted people to obtain their birth certificates as soon as possible.
According to the Department of Health the question of access to records was being considered in the "wider context". A department spokesperson said the new computerised registering system was being looked at in a way that would reflect the concerns of all those involved. The APA claimed the computerised system, as originally designed, was capable of performing such searches.
Mr Sweeney, a former computer programmer, said there was no technical problem involved - he could even provide the two-lined computer code that would allow such searches to be implemented.
The APA will campaign to ensure the new system will allow adopted people to obtain their birth certificates independently - quickly, easily and efficiently.
They have also asked for a meeting with Health Minister Micheal Martin, in a bid to persuade him to accept their position.