Thanks for bringing your question to JustAnswer.
"Should I just give up on it and forget them?" That is certainly an option. It can be confusing when we act in innocence and yet someone gets mad.
I have no idea why the baby's mother has cut her father out of her life, but she has made that choice clear. Facebook allows a page owner to determine who is allowed to see what is posted...that's why many people set their page to "friends only" ...to be able to post things, but still have some privacy, some control over who sees their page. So, in their eyes, it may seem as if you disregarded their wishes for privacy..
With all the losses you have suffered recently, I would advise against cutting them out of your life. If you do, you would lose out on getting to see this precious baby.
You might consider letting them know that you are sorry for not realizing they didn't want the dad to see the pictures...didn't realize about privacy settings, etc, rather than say that they never told you you couldn't . That may be the truth, but it will only fan the flames of the hurt she is feeling. She may be feeling that since you know how she feels about her father, that you would then understand that she doesn't want him to have any connection to her baby's life. Also try to remember how sleep-deprived and emotional new mothers are.
Sometimes, it is better to apologize in order to keep people in your life. Even though you are technically right, it will be better in the long run to be happy rather than right. Assure her you will not share any information with the dad in the future. I know you are stinging from their lashing out at you, but don't cut them out of your life at a time when you have just gone through such a painful loss. You have lost enough already, and will want this connection to them in the future.