From their website:

“It is critical that any new Justice empathize with the true plight of women to not only recognize when those protections are being violated, but to take steps to safeguard them. We encourage the Senate Judiciary Committee to engage Judge Sotomayor and any future nominees to the Court on their commitment to the principles of Roe v. Wade. Anything less threatens not only a woman’s constitutional rights, but her life and health.”
Judge Sotomayor has not ruled on the constitutional right to abortion. However, in 2002, she authored an opinion in a case brought by the Center for Reproductive Rights (at that time the Center for Reproductive Law & Policy), challenging the reinstatement of the Global Gag Rule or “Mexico City Policy,” which prohibited overseas organizations that received U.S. funds from providing abortion services or engaging in speech intended to ease restrictions on abortion. The Center filed Center for Reproductive Law & Policy v. Bush on behalf of itself and its attorneys asserting that the Center’s work overseas with women’s rights organizations seeking law reform to address the deaths and harmful consequences of unsafe abortion would be hampered by the Global Gag Rule. Writing for a three judge panel, Judge Sotomayor relied on previous Second Circuit and U.S. Supreme Court decisions to reject the Plaintiffs’ First Amendment, Due Process and Equal Protection claims. The opinion focused on the application of legal precedent and did not express a view on or discuss the impact of the Global Gag Rule on abortion law reform efforts around the world.