First of all, don't let the media drive the thought process over Laudato Si’ (Praise Be to You). It has a selfish motive, the same selfish motive which drives much of its coverage of religion: it wants to harm all genuine faith and marginalize it in the secular world. Remember too it has been wrong before in its reporting of what the Pope has said. Read the letter without regard for what media outlets assert.
To conservative Catholics, it is important that you not reject its teaching simply because you may fear they are errant. You've often accused liberal Catholics of being the cafeteria kind: picking what they want out of the faith while ignoring what they don't personally care to support. If we expect them to at least seriously and prayerfully consider the instructions of Humanae vitae, Pope Paul VI's famous instructions against artificial birth control, then you must not reject the correct core teachings of Laudato Si'. We'll venture to guess that they aren't so bad anyway.
Back to the more general audience, it should be pointed out that good stewardship is a good thing. We are not within our rights to run rampant over the Earth. While we may rightfully argue for private property as the best kind of stewardship we must recall that no less that St. Thomas Aquinas taught that even private property should be held as public. We must treat what is indelibly ours as if it belonged to everyone. This belief does not run contrary to Catholicism, conservatism, or even libertarianism at all. We cannot imagine that the Pope has in fact, in an important teaching document, strayed that far from faith and reason himself.
We'll say more as time goes on and we read the letter ourselves. But for now our advice is: liberals and secularists, don't, ahem, read too much into this. Conservatives, don't you either.