There is absolutely no truth to this statement whatsoever. The "right of privacy" that was the basis of Roe v. Wade was actually an extension of the "right of privacy" that was first discovered (i.e., made up) by the U.S. Supreme Court in a prior case (I believe it was Griswold v. State of Connecticut) involving a state law against selling contraceptives. There is absolutely no basis in Constitutional law for this "right of privacy," so as far as the U.S. Constitution is concerned each state has the right to regulate the production and sale of contraceptives as it sees fit.
Of course it is lost on most Christians today that until 1930, ALL of JUDEO-CHRISTIAN morality, including orthodox judaism, Catholicism, Orthodox Christianity, and Protestantism, taught that contraception was inherently evil, without a single exception. The Comstock laws, overturned in the SCOTUS decision of Griswold Vs Connecticut, which formed the philosophical underpinnings of R v W, were written in the 1800's by protestant legislators, NOT Catholics. (The only debate is whether the protestant capitulation to the contraception agenda, from 1930 to 1960, was "wisdom" or heresy/apostacy.)