Finding an obiettore is a somewhat rare circumstance in a hospital, but it's unlikely in a consultorio familiare; those are structures whose only purpose is reproductive health, gynecological care, social services, and psychological consult, especially aimed at teens and women. If you're an objector you generally don't go out of your way to work there.

I’m sure you’re aware that it _greatly_ depends on the region you’re living in. The fact that consultori are for reproductive health doesn’t mean that there are no obiettori: for some of them the purpose of those structures are exactly to prevent abortions. There are many accounts of women who were pushed to not interrupting a pregnancy.