I was a little surprised to find that some contemporary Americans are naming their miscarriages and burying them in cemeteries.
I hypothesize that this is related to the abortion debate in the US, in that if you are going to frame an embryo as a human life from the moment of conception, you'd be inclined to do the same thing in relation to spontaneous abortion, also known as miscarriage, in order to bolster that case.
How correct is this? Or, more specifically, were Christians or early Jews commonly treating miscarriage with as much gravity as the death of a child, at any time prior to the Roe v Wade decision?
Since you asked about Jewish opinions, Judaism doesn't treat miscarriage as a child's death--there aren't mourning rituals involved. In fact, mourning rituals aren't even mandated for an infant who dies before 30 days of life. While classical Jewish sources do sometimes regard miscarriage/stillbirth as a grief-inducing thing (as with David in the bible), it's not regarded as a person dying.
For a more general discussion of the status of fetuses in Jewish texts, see my comment here.