Participatory democracy involves more than voting in elections. The bishops see the importance of organized groups that are not part of the government, what is often called civil society. These play a role similar to the “intermediate institutions” that Alexis de Toqueville found in the United States in the early nineteenth century.
They particularly note several groups which have been organizing in recent years, exerting influence in the public sphere, and being less marginalized.
Participatory democracy is growing stronger with the more assertive presence of civil society, and the emergence of new social actors, such as indigenous people, Afro-Americans, women, professionals, a broad middle class, and organized poor people, and more room for political participation is being created. These groups are becoming aware of the power they hold in their hands and of the possibility of bringing about major changes for achieving more just government policies, which will reverse their situation of exclusion.
But the bishops have a few concerns about the direction of civil society.
In this regard, a growing influence of United Nations agencies and international non-governmental organizations is evident, although their recommendations are not always in line with ethical criteria. Their actions sometimes radicalize positions, foster extreme confrontation polarization, and place this potential at the service of interests foreign to their own. In the long run their hopes could be frustrated and negated.
What might the bishops be referring to?
I am going out on a limb and suggesting that this might be related to concerns about “radical feminism,” “homosexual rights,” and other related issues. They also might be a bit concerned about the promotion and support by non-governmental organizations of civil society organizations in conflict situations in Latin America, particularly over land, mining, and some environmental concerns.
Here is an English translation of the 2007 document from the Aparecida Conference.
Catholic Sensibility 
“What might the bishops be referring to?”
Your guesses are correct. Additionally, NGOs and the UN have also pushed contraception and abortion in Latin America.
Knowledgeable, medically supported and wide-spread use of contraception is of course one way of bringing down the abortion rate.
But since most uses of contraceptives are evil in themselves, it should not be promoted as an abortion alternative.
But since most uses of contraceptives are evil in themselves
And what exactly are those “evil uses”? Alleviating the severe maternal health problems and/or early deaths which are often the result of frequent, close-spaced births? Ensuring that parents can actually provide reasonable material support for their children? (Allow me to point out, by the way, that this consideration often does not occur to celibate religious persons, who have been supported from early adulthood by the contributions of the faithful…). Safeguarding potential children from the often lifelong emotional damage caused by “parents” who don’t, in fact, want a family…. and who take out their resentment on helpless youngsters? Providing at least some protection for heedless adolescents against their own unregulated impulses – and protecting the baby otherwise entrusted to a hapless mother of 16 or 17, whose father is probably absent?
Glib nostrums about chastity or how we must trust in the Lord to provide are about as useful, outside the world of a holy picture card, as the trite – and patently untrue – belief that a new parent, however reluctant they may have been before the birth, will inevitably fall in love with their child. The Church, by ignoring reality as blatantly as it has done since 1967, has largely created for itself the current situation in which *it* is ignored or disdained by so many. I trust that the upcoming Synod on the family will at least begin a reconsideration.
Finally, contraception isn’t an *alternative* to abortion – it helps *prevent* abortions.