Back in the 90s, I had to help my mother get her birth certificate from Arkansas. I called the county she was born in and asked the clerk.
The woman was very polite, but she searched and searched...no birth certificate for my mother could be found. She asked me to call back the next day, while she would continue to look.
The next day...she still couldn't find it. Nor had she found it the day after that.
Finally, she hesitated a moment and then asked, "Pardon me for asking...but is your mother black?"
I said, "Yes."
She said, "Oh!" Then five minutes later: "I found it!"
The birth certificates in that county were still separated by race (at least those dating back to when they were separated by race).
Also in the 90s, I had the opportunity to do some community service in Montgomery, Alabama, that involved a young elementary school teacher and I going through old county school records stored in stacks and stacks of boxes, putting them in order so a team could properly file them. We had spent most of the day working on the records when we finally got to one of the boxes in the very back of the room. After a while as we tallied the records in that box, the young teacher, a white woman from North Dakota, suddenly noticed that all of them had listed the race as "colored"...which hadn't been noted in any of the other boxes, but was consistent on all the records in this box.
I had already noticed that...and I understood why, which I had to explain to the young lady. I also already knew that in those years, such school records were the only records black people often had.
I suspect there are lots of birth certificate issues for many people who were born in rural areas fifty or more years ago, and particularly if they were the records of blacks stuck in a separate box.