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First, note that the 39 Articles are a creation of the English reformation of the Sixteenth century, having been put into their present form in 1563, and while they have the force of Law in the Church of England, they have a lesser authority in other political jurisdictions, and have been controversial since the beginning. There have been articles to which various factions objected from the beginning, and I suspect that there would have been Anglicans from the 1500's who might have objected to the Calvinist tone of Article XVII.
Furthermore, in this consideration, the second paragraph (which was supplied in the original question, and which I have replaced with the entire article) should not be divorced from the first paragraph of the article as the context of the second paragraph depends very greatly on the first paragraph, and in particular the opening of that paragraph: "Predestination to life is the everlasting purpose of God,..."
Second, the question as posed by the original poster presumes that there is a universal Anglican position on this article. There was not at the time it was written, and there still is not today. One can without much difficulty find Anglican divines and theologians on both sides of the question. While there are undoubtedly some Anglicans who might answer in the affirmative, there are others (Arbishop Tutu comes to mind) who would deny that it is the case, and who would ascribe the moral meltdown of society to other influences.
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Two Australian Anglicans, Michael Jensen and Tom Frame, interpret that part of the article to not be saying that the doctrine causes people to sin, but that it is a warning that people can misuse the doctrine and turn it into a kind of fatalism that produces desperation and licentiousness. What is always needed is more solid Biblical teaching that will correct any distortion of the doctrine to both encourage us and rebuke us when we need it.
The thought that somehow God chose some people and not others long ago, even 'before the foundation of the world' (Ephesians 1:4), is an idea that many people have found distinctly uncomfortable. It seems to pit God's sovereignty against God's love. It vexed those living in the sixteenth century as well. For them the question was more existential: if I am one of God's chosen people, then what are the signs confirming that status? How can I know that I am one of the elect? What if my name is not written in the Book of Life? This became a significant pastoral problem as well as a matter of theological dispute. The article itself issues a warning about the 'curious and carnal persons' who misuse this doctrine and end up in the grip of a kind of fatalism - that produces either psychological desperation or moral licence.
Yet the article does not treat this teaching as an ethical embarrassment nor as an academic puzzle. It is when rightly considered ('godly consideration'), a 'sweet, pleasant and unspeakable comfort.' It is actually of great pastoral help because it gives the Christian great security in God.
Source: Defining Convictions and Decisive Commitments by Michael Jensen & Tom Frame, pages 59-60.