It must be hard to have that phobia and have people understand--maybe you need to be super-honest and say you have a truly clinical phobia of babies.

Although I like babies, I think their cries are deeply unsettling too. I think it must be instinctual for women--the cry turns on an alarm that cries DO-SOMETHING-NOW!!
Their cries are eerily not quite human or animal. They are fragile, wobbly. I get that.

Ever read about the notion of "uncanny valley"?? It is what makes us feel uneasy about human like robots, mannikins or bad special effects, even clowns. Something appears almost-human but something nags at you that something is off and not quite right. No one has been able to create a humanoid robot that isn't freaky for this reason. Wondering if that concept applies to your fear of babies?

sorry if this link is too much--just a trigger warning just in case
10 Creepy Examples of the Uncanny Valley