We're very comfortable with our bodies, and as a result, so is our daughter. As far as she is concerned, a penis or vulva is no more interesting than a foot or an elbow. I think that when adults react uncomfortably, though, that is interpreted by children, whether it's someone who never undresses in front of anyone and is uncomfortable being seen naked, or someone who is uncomfortable answering a child's questions. Sometimes (almost always?) it is not what you say, but the manner in which you say it.
Children usually develop a sense of modesty around 6 or so, but until then, they're all curious and our responses and reactions inform them both factually and emotionally. Is the bathroom door left open and your child wanders in-and-out freely while you shower and bathe, or do you close the door and grab a towel and shreik when she walks in? What messages do these things send about your bodies and hers? Do you respond matter-of-factly to questions or do you get flustered and evasive?
If it makes your partner very uncomfortable and anxious, then he should stop. Better to avoid the situation (for now) than to unintentionally telegraph his discomfort to her. Just curiously, if she were a boy would he feel this way?
OTOH, I know that there are many women who were abused as children and struggled with the decision to breastfeed, ultimately coming to the conclusion that they would not allow the abuser to effect their children as well.
Not feeling too coherent today. Those are my random thoughts for now!