Final answer:
The movement centered around the rights to have an abortion, to have children, and to parent is known as Reproductive justice. It is part of a broader rights movement focused on reproductive and parental rights, distinctly separate from but occasionally intersecting with LGBTQIA rights.
Step-by-step explanation:
The movement described by the core values of the right to have an abortion, the right to have children, and the right to parent those children refers to Reproductive justice. This is a broader social movement which covers the right to have a child, not have a child, and parent children in safe and healthy environments. It is deeply connected to the rights of women and often intersects with other social issues.
While the LGBTQIA rights movement shares some intersecting issues with reproductive justice, such as the right to marry and the right to free exercise of religion, they are distinct movements with different core objectives. LGBTQIA rights have significantly progressed, as seen in the legalization of same-sex marriage and the wider acceptance of LGBTQ individuals.