Explains the idea better than I can
Links in that post can explain in great detail the Church's position on female ordination, abortion/contraception, and homosexual relationship & marriage
Judging men by the standard of today is a very unfair thing to do. The Pope and the Magisterium are only infallible on matters of faith and morals under special circumstances. Not everything the Pope says or teaches is infallible.
And yes, I know about the Papal Encyclicals in defense of slavery. They are not infallible. Binding? Yes. But only at the time they were written during the circumstances in which they were written. The Popes that wrote the Encyclicals on slavery were wrong. They succumbed to the pressure of foreign governments. The Pope is just a man. The Church's defense of the African slave trade was wrong. The Church's defense of slavery for the first 1000 years or so before the African slave trade is wrong to us today.
This explains it:
In ancient times, slavery was seen as justly arising from one of three circumstances: (1) capture in war, (2) punishment for crime, and (3) obligation for debt. Enslavement for debt would be the least reconcilable to Catholic doctrine, although the Church had to deal with it as an historical reality in Roman law, reacting prudentially in order to mitigate the evil without creating greater ones. Regarding prisoners of war, however, more deserves to be said. Biblical slavery could be seen as a reform, a lesser evil made necessary by the inability of societies to hold war prisoners in idleness due to scarcity of resources. Release of prisoners was extremely impractical when wars lasted many generations, as did Israel's wars with her hostile neighbors, the Greek struggles with the Persian Empire, or the Punic Wars between Rome and Carthage. Humane slavery (always a Catholic requirement) was a superior option to the suicidal release of prisoners of war, the economic impossibility of simply imprisoning war captives, or the terribly inhumane alternative of executing captured enemies.
It is important to note that the Catholic Church in past centuries did not intend to endorse authoritatively any specific instances of slavery, but only the principle that slavery could be justified as the lesser of evils in certain circumstances. The situation surrounding ancient warfare illustrates one particular application of this principle. The same notion of the "lesser evil" was also applied to the question of the status of the children of slave mothers. As Noonan observes, "St. Antoninus of Florence followed St. Thomas in acquiescing in the civil law permitting slave status to follow birth to a slave woman,"20 but in noting that the eminent Jesuit moralist Cardinal Juan De Lugo "found slavery 'beyond the intention of nature,' but 'introduced to prevent greater evils,'"21 Noonan does not see the clear extension of that principle to the conveyance of the mother's status to the children.
One can easily see that if the Church had attempted to bestow freedom upon the children of slaves, owners might well have denied the right of slaves to marry, with all the attendant evils that would involve, and owners might not have properly cared for the offspring of slaves . . . offspring over whom they would have enjoyed no property right.
Thus, we can see the complicated case for accepting slavery as a social condition arising from prolonged periods of warfare. John Locke's justification of slavery in his late 17th-Century work, Two Treatises on Civil Government, contains the same rationale as has been given here. 22 It will be recalled, of course, that much of modern slavery did not so originate, since innocent and non-belligerent persons were set upon (usually in Africa) and impressed into slavery without moral justification and in the most inhumane of conditions.
Finally, classical morality accepted the legitimacy of slavery for crime. This form of slavery, it would seem, can be easily justified, and under a different name, this penal slavery is still the practice of most nations. It is not accidental that in the aftermath of the American Civil War, the framers of the Thirteenth Amendment to the U.S. Constitution wrote into that amendment an exception to the prohibition on involuntary servitude. The text of the 13th Amendment states, "Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist . . . ." Prisoners may be compelled to work, their liberties are often seriously curtailed, and although the vast majority remains in this condition for only a limited period of time, "life without parole" is an increasingly used option, as are finite sentences of such duration as to ensure that they constitute de jure life imprisonment.
The change of the Church's attitude toward slavery reflects the changed circumstances of the world more than it reflects any revolution in moral theology. Wars tend to be of shorter duration in the modern world (though often of far greater severity); nations often possess surpluses out of which they can feed and care for prisoners of war who are held as prisoners rather than as slaves as would have been the case in previous times, and most importantly, perhaps, civil authorities are willing, in general, not only to abolish slavery, but to extirpate those greater evils the avoidance of which made slavery's existence permissible. In this new environment, the Church may put greater emphasis on its statements that "slavery is evil" . . . but it had never judged otherwise. The Church had done no more than proclaim that in other sets of social and historical circumstances, slavery represented the lesser of evils.
Anyway, to get back to the point of the OP, the Church is not evil or bigoted for telling the group of nuns that they need to conform to doctrine. As I've said before, if the nuns or any priests don't feel as if they can support the Church because of a these issues mentioned in the OP article, then they can become Episcopalians where all those things are allowed.