My thoughts?  This is the fruit of Dignitatis Humanae as the direct departure from the Church's true teaching on relations between non-Christians and the civil state.

First, one must understand the concept of a right, insofar as it is understood philosophically.  A right, as defined by the Cambridge Dictionary of Philosophy is:

"Rights are advantageous positions conferred on some possessor by law, morals, rules, or other norms."

Naturally, it must follow that a right, as created and bestowed by God, is such that the advantage of its proper exercise is that it confirms and enriches man's communion with God, for the purpose of his perseverance in grace to the end of his life, and that strengthens the orderly association with his fellow man in Christian society.

Second, one must understand how Dignitatis Humanae perverts the just and natural supremacy of the Holy Faith in the natural affairs of men.  It is permissible, for the sake of civil order, to tolerate the private exercise of non-Christian religions, that much is true.  But Dignitatis Humanae stated that the freedom of man to publicly profess the religion suited to his belief and conscience was a fundamental right, as it states:

"This Vatican Council declares that the human person has a right to religious freedom. This freedom means that all men are to be immune from coercion on the part of individuals or of social groups and of any human power, in such wise that no one is to be forced to act in a manner contrary to his own beliefs, whether privately or publicly, whether alone or in association with others, within due limits." (And to those that would argue that any heresy or error in DH is restrained or mitigated by the limitation clause at the end, may we be honest with one another that this is nothing more or less than a modernist attempt at an appearance of restraint?)

"Therefore the right to religious freedom has its foundation not in the subjective disposition of the person, but in his very nature."

Now, a natural or indelible right is something due to a creature of virtue of its nature.  God created man, God is man's beneficence, and God alone is due the honor and glory of man's worship and obedience.  To say that man has been given an indelible right to choose any religion, even a false one, by God is blasphemous and heretical because it suggests, either:

1.) That the Christian religion is the only means by which man can be saved, though God has permitted man the right to choose a false religion, meaning that the advantage, name salvific potential, to the exercise of religion is selective, putting a lie to the assertion: For this is good and acceptable in the sight of God our Saviour, Who will have all men to be saved, and to come to the knowledge of the truth (1 Timothy 2:4)

2.) That the Christian religion alone is not the only means by which man can come to true knowledge of his Creator, His morality, His law, the means by which he can be reconciled to Him, and the fruits of that redemption.  Incidentally, such a notion contravenes John 14:6, though the attempt to mitigate this is addressed shortly.

In point of fact, the modernist aim is the second, as it is fundamental to the false, Vatican II religion, for it is on that foundation that rests its preoccupation with universal salvation.  If man does not have the right to choose a false religion then that selection, willfull and intelligent, is sufficient to damn him, for he has violated the prescription of God to persist alone in the Holy Catholic faith.  Conversely, if man does possess that right, then he does not contravene the prescriptions of God, insofar that he could, by living as just a life as possible and cooperating with those "elements of salvation" found in his religion, as suggested by Lumen Gentium, be saved by the nebulous union "in some invisible way" with the Church of Christ, as understood and beloved of the modernists, and necessary to reconcile its perfidious pluralism with Christ's rightful role as sole mediator between God and man.

Now, the fruit of both Dignitatis Humanae and Lumen Gentium is the devolution of primacy and singularity of the Holy Catholic Faith as the means of men's salvation, and of the Roman Catholic Church as the first, last and only organ by which the Faith is preserved, interpreted and transmitted.  This devolution, a gross and deformed flowered bloomed from the seed of the indifferentism of the Americanist heresy, finds its purchase in the reduction the Catholic faith to equal standing as regards other religions and, by extension, its equal submission to the whims of civil law.  In decrying the primacy of the Christian religion, in relinquishing its supremacy over civil law and as the definer of public good and morality, it now finds itself at the point of the very gun by which it destroyed all hope and exercise of civil and moral order.

So, let's say that a dioceses(new Order) is asked by the Federal gov't, "would you like to get money to survive, that is, for your every $1. we will give you $3.  Just keep your "identity" (name only) and follow our directives, say, contraceptives and etc in your hospitals, clinics. And you can not say anything political and such, and sign on the dotted line."  Now, If a Bishop of his dioceses does such, he has used his freedom to choose, God or Man. I see that is where things are and for a Bishop to say he is supporting Church teachings in this area, he is deceiving.  The Federal gov't is not the problem, it is the Bishops.

The conciliar establishment is already in that situation, insofar as those health care institutions that label themselves Catholic are concerned.  In reality, the retention of the Catholic title for hospitals is merely for cultural or financials reasons; many conciliarists have a lot of money to throw at charities and they try to support those that are ostensibly Catholic.  Nonetheless, I would venture that most, if not all "Catholic" healthcare institutions participate in government-funded medical programs (Medicare and Medicaid), which by virtue of law makes them subject to federal mandate regarding provision of health care services.  Insofar as the Federal government is concerned, neither abortion nor contraception is illegal (I do not say immoral as the American legal system has no recourse or foundation in Christian morality), those institutions that receive money from the government are legally enjoined to provide those services which the government, as provider of funding, establishes as vital.

The problem is that the conciliar establishment, lacking the supernatural charity that is indicative of the true Church of Christ, abdicated its mandated duty to tend to the sick to the Federal government.  Catholic hospitals, run by conciliarists, ceased to be the refuge for the sick, the dying, the chronically ill, and those without resort.  They became businesses of profit and, eventually, cogs in the godless machine of institutionalized death, factories of chemical and surgical abortion, of euthanasia, of murder for the profitable harvesting of organs.  What's happening to them now is the just result of that abdication.

The same is true of Catholic business that use government-funded healthcare programs.  They are required to permit all services that are funded by the government irrespective of how they might conflict with Catholic doctrine.