Let's not overlook these either:
14. The contention, then, that the civil government should at its option intrude into and exercise intimate control over the family and the household is a great and pernicious error. True, if a family finds itself in exceeding distress, utterly deprived of the counsel of friends, and without any prospect of extricating itself, it is right that extreme necessity be met by public aid, since each family is a part of the commonwealth. In like manner, if within the precincts of the household there occur grave disturbance of mutual rights, public authority should intervene to force each party to yield to the other its proper due; for this is not to deprive citizens of their rights, but justly and properly to safeguard and strengthen them. But the rulers of the commonwealth must go no further; here, nature bids them stop. Paternal authority can be neither abolished nor absorbed by the State; for it has the same source as human life itself. "The child belongs to the father," and is, as it were, the continuation of the father's personality; and speaking strictly, the child takes its place in civil society, not of its own right, but in its quality as member of the family in which it is born. And for the very reason that "the child belongs to the father" it is, as St. Thomas Aquinas says, "before it attains the use of free will, under the power and the charge of its parents."(4) The socialists, therefore, in setting aside the parent and setting up a State supervision, act against natural justice, and destroy the structure of the home.
15. And in addition to injustice, it is only too evident what an upset and disturbance there would be in all classes, and to how intolerable and hateful a slavery citizens would be subjected. The door would be thrown open to envy, to mutual invective, and to discord; the sources of wealth themselves would run dry, for no one would have any interest in exerting his talents or his industry; and that ideal equality about which they entertain pleasant dreams would be in reality the levelling down of all to a like condition of misery and degradation. Hence, it is clear that the main tenet of socialism, community of goods, must be utterly rejected, since it only injures those whom it would seem meant to benefit, is directly contrary to the natural rights of mankind, and would introduce confusion and disorder into the commonweal. The first and most fundamental principle, therefore, if one would undertake to alleviate the condition of the masses, must be the inviolability of private property. This being established, we proceed to show where the remedy sought for must be found.
7. This becomes still more clearly evident if man's nature be considered a little more deeply. For man, fathoming by his faculty of reason matters without number, linking the future with the present, and being master of his own acts, guides his ways under the eternal law and the power of God, whose providence governs all things. Wherefore, it is in his power to exercise his choice not only as to matters that regard his present welfare, but also about those which he deems may be for his advantage in time yet to come. Hence, man not only should possess the fruits of the earth, but also the very soil, inasmuch as from the produce of the earth he has to lay by provision for the future. Man's needs do not die out, but forever recur; although satisfied today, they demand fresh supplies for tomorrow. Nature accordingly must have given to man a source that is stable and remaining always with him, from which he might look to draw continual supplies. And this stable condition of things he finds solely in the earth and its fruits. There is no need to bring in the State. Man precedes the State, and possesses, prior to the formation of any State, the right of providing for the substance of his body.
8. The fact that God has given the earth for the use and enjoyment of the whole human race can in no way be a bar to the owning of private property. For God has granted the earth to mankind in general, not in the sense that all without distinction can deal with it as they like, but rather that no part of it was assigned to any one in particular, and that the limits of private possession have been left to be fixed by man's own industry, and by the laws of individual races. Moreover, the earth, even though apportioned among private owners, ceases not thereby to minister to the needs of all, inasmuch as there is not one who does not sustain life from what the land produces. Those who do not possess the soil contribute their labor; hence, it may truly be said that all human subsistence is derived either from labor on one's own land, or from some toil, some calling, which is paid for either in the produce of the land itself, or in that which is exchanged for what the land brings forth.
9. Here, again, we have further proof that private ownership is in accordance with the law of nature. Truly, that which is required for the preservation of life, and for life's well-being, is produced in great abundance from the soil, but not until man has brought it into cultivation and expended upon it his solicitude and skill. Now, when man thus turns the activity of his mind and the strength of his body toward procuring the fruits of nature, by such act he makes his own that portion of nature's field which he cultivates -- that portion on which he leaves, as it were, the impress of his personality; and it cannot but be just that he should possess that portion as his very own, and have a right to hold it without any one being justified in violating that right.
10. So strong and convincing are these arguments that it seems amazing that some should now be setting up anew certain obsolete opinions in opposition to what is here laid down. They assert that it is right for private persons to have the use of the soil and its various fruits, but that it is unjust for any one to possess outright either the land on which he has built or the estate which he has brought under cultivation. But those who deny these rights do not perceive that they are defrauding man of what his own labor has produced. For the soil which is tilled and cultivated with toil and skill utterly changes its condition; it was wild before, now it is fruitful; was barren, but now brings forth in abundance. That which has thus altered and improved the land becomes so truly part of itself as to be in great measure indistinguishable and inseparable from it. Is it just that the fruit of a man's own sweat and labor should be possessed and enjoyed by any one else? As effects follow their cause, so is it just and right that the results of labor should belong to those who have bestowed their labor.
See, Leo is talking, in paragraph 37, about the government's role in helping people maintaining their rights. Leo asserts that the rich have the resources to protect their rights but that the poor do not. But what rights?
I personally can't see where those rights defined above (with references) are at all in opposition to conservatism.
It is only through the most tortured reading of Rerum Novarum where one asserts that Leo XIII makes a claim for Nanny-Statism.