"The nature of the embryo is at least as objective as their intent and statements."
The embryo, or slightly thereafter is not a person until they announce that it is. Otherwise it is human life only insofar as every other cell in a human organism is. Personhood is a concept, not a biological characteristic. The decision regarding personhood belongs to the parents, until such time that the concept of effective contraception is no longer a valid.
The concept of personhood is based on objective facts rooted in biology. If it were up to the decisions of others, then the Nazis should have been left free to act on their decision that Jews, gypsies, and others were Untermenschen, subhuman.
The decision regarding personhood belongs to the parents
That wouldn't follow even if we accepted that personhood is unrooted in objective reality. Why just the parents, when the whole of society is affected by the 40 million lives lost to abortion?