I have never liked children or wanted any of my own. I understand how it feels to find something extremely cute and adore something at first sight (I get this feeling with many animals), however when it comes to human babies and children, all I feel is at best a complete absence of emotion, or worse (depending on the parents' tolerance of uncleanliness), mild disgust. This isn't something which is on the level of a values judgement (i.e. I don't think people should not have children), it is just that my emotional reaction to children goes against that of mainstream society.
I have one friend who has recently had a child. I found it was very easy and natural to continue our friendship during her pregnancy -- I don't love talking about children, but while she was pregnant, it was easy to care about her health and physical condition and fears and hopes for the future. Hers, not really the baby's. I was also very happy for her, because I knew it was what she wanted and although I couldn't intuitively understand why having a child would make her happy, it was enough for me to know that it would.
However now that she has had the child, I'm nervous about how to keep our friendship. On one hand, I want to stay friends and this includes hanging out and being there for her through the challenges of parenting. On the other hand, it seems inevitable that doing this will mean I need to interact with the baby. In these interactions, I don't want to have to pretend that I like children, or that I find her baby cute, or that I want to play with her baby, hold it etc. I don't think I could fool anyone even if I pretended...
So how could I convey both of these desires to her with as little awkwardness as possible, and avoid offending her? Generally new parents seem head-over-heels in love with their children and expect others to also be. I want her to know this is nothing personal without triggering an emotional reaction.