"... they can then go after abortion".
Then contraception and IVF.
Then "non-traditional" roles and family models such as non-stay-at-home women and same-sex relationships ...
Exaggerated?
The papers are out there, e.g. "Dignitas Infinita" (The Pope) and "Plan 2025" (The Heritage Foundation). Fidesz laws and proclamations (Hungary), anybody?