The child SHOULD have the skills required to nap differently in different places. When this is the case nursing before sleep in one location should have NO impact on their sleep elsewhere. They should have the skills needed to self sooth and sleep while still being able to rely on parents at home. Nursing on demand at home is perfectly fine if the child has been given the skills needed function elsewhere.
AP parenting does not need to be all or nothing. If they planned ahead and provided the child with the skills needed then they would be able to nurse non-stop at home, co-sleep and all that great bonding stuff without an impact on daycare. This is, again, where I feel AP has taken a wrong turn. AP parenting is supposed to be about raising emotionally attached, self confident happy, and ultimately independent children. It is not about raising demanding, incompetent 'terrors'...which is often how things seem to be going these days.