Positive as an adjective has a variety of nuanced meanings. I will attempt to sum them up and interpret your quote based on a few.
1. consisting in or characterized by the presence or possession of features or qualities rather than their absence.
constructive in intention or attitude.
"there needs to be a positive approach to youthful offenders"
The Vatican is warning Catholics to be constructive in their handling of marriage issues and unmarried people living together, as opposed to their historical approach of ostracizing and casting out. This is a probable intended connotation, given positive appears in the same sentence as sensitivity.
Furthermore, the section you quote is under Part III The discussion: pastoral perspectives, which contains other headings such as
- Proclaiming the Gospel of the family today, in various contexts
- Guiding couples on the path in preparation for marriage
- Accompanying the early years of married life
And the section 36 is cribbed from
- Positive aspects of civil unions and cohabitation
showing optimism and confidence.
"I hope you will be feeling very positive about your chances of success"
showing pleasing progress, gain, or improvement.
"the election result will have a positive effect because it will restore people's confidence"
Unlikely, given that Church sanctioned weddings are still preferred and cohabitation (which I assume means unmarried people living together - with the further unstated assumption that they are sexually active outside of wedlock) is considered a sin. The Vatican is not optimistic about the spread or prevalence these things, and while the Catholic Church may no longer be treating it as the Devil's work, they are far from encouraging it.
2. with no possibility of doubt; clear and definite.
"he made a positive identification of a glossy ibis"
convinced or confident in one's opinion; certain.
"“You are sure it was the same man?” “Positive!”"
informal downright; complete (used for emphasis).
"it's a positive delight to see you"
This is the likely intended denotation of the phrase "positive reality". Civil weddings and cohabitation are every day occurrences in modern society, a fact that cannot be changed by any amount of denial.
The synodal document you link goes on to include the following sections.
37. It was also noted that in many countries [unmarried cohabitation is an experiment]. Faced by these situations, the Church is called on to be “the house of the Father, with doors always wide open […] where there is a place for everyone, with all their problems” (Evangelii Gaudium, 47) and to move towards those who feel the need to take up again their path of faith, even if it is not possible to celebrate a religious marriage.
38. In the West as well there is an increasingly large number of those who, having lived together for a long period of time, ask to be married in the Church. Simple cohabitation is often [caused by societal attitudes or norms, or circumstances beyond the control of the couple, such as poverty]. [In] such unions it is possible to grasp authentic family values or at least the wish for them. Pastoral accompaniment should always start from these positive aspects.
39. All these situations have to be dealt with in a constructive manner, seeking to transform them into opportunities to walk towards the fullness of marriage and the family in the light of the Gospel. They need to be welcomed and accompanied with patience and delicacy. With a view to this, the attractive testimony of authentic Christian families is important, as subjects for the evangelization of the family.
To me, that says the broader message is that people who pursue marriage arrangements outside of traditional Catholic norms should no longer be excommunicated, shunned or blamed. Instead, they should be counseled and encouraged to remain as active in the Catholic Church as possible. The use of the superlative positive reality may have been intentionally included by the translator to set the tone and include connotations beyond the most probable meaning that cohabitations and outside church marriages are real. But as others have pointed out, since this is a translation, we can only speculate as to the exact intended meaning in English.
All definitions taken from Google.
