This thought may be way off, but if the birth mother was very young, and the adoptive parents were insistent that your friend does not try to trace the birth mother, the first thing that comes to mind is that the adoptive parents may have been her grandparents. Did your friend have an older sister?
I feel by making your friend promise not to trace her birth parents, that might lead her to being even more curious.
There are a couple of ways to view this. Yes, your friend wants to keep her promise to her adoptive parents which is commendable, but also was it right that her adoptive parents made her make this promise in the first place? Presumably it was some years ago, and it would have been a different era with different morals and expectations, so understandable, but still very hard for your friend who probably needs to consider her own wishes as well. Yes, they may have been trying to protect her from something, especially while she was young, but for some people finding out the truth understandably can become an obsession especially as they get older. If your friend is curious about her birth family I don’t know that she should deny herself trying to find the answers she is looking for, though she should be aware that she may not like what she finds.
Some people are prepared to take that risk nevertheless.
It could be that no one would bat an eyelid today whatever the story behind this is. I’m sure many of us have similar secrets in our families which we think nothing of but which would have been shameful a couple of generations ago.
In commencing any such search, it may be significant how long ago her adoptive parents died and whether or not she has other siblings or extended family who may not approve if they were aware of what she was doing (and of course she can choose whether or not to tell them - after all, this is her personal journey).
Interesting dilemma - I’m sure we all have different opinions, but in the end it is her family and their promise (or secret) so your friend needs to do whatever she thinks is right. As already suggested, if she is interested in tracing her family history maybe tracing both adoptive and birth families might ease any guilt she may have for perusing this.
I hope she feels comfortable with whatever decision she makes. Good luck to her.