This should be achieved through "new pastoral attitudes", according to a letter from the cardinal, which was read out at an event organised by the Global Network of Rainbow Catholics (GNRC) on Sunday.
Cobo also called on the Church to avoid any form of discrimination against LGBTQ Catholics.
The conference took place from 22 to 26 August in Madrid and brought together around 160 participants from Africa, Asia, Australia, Europe, Latin America and North America. It was the fifth event of its kind and was held under the motto: "Travelling together: rainbow challenges after the Synod".
Developing new pastoral attitudes
Cobo, who is also Vice President of the Spanish Bishops' Conference, emphasised the central importance of the person and their dignity, "which should be decisive for all Christians".
He went on to explain: "In addition to reception, we must promote a culture of dialogue, accompaniment and effective inclusion - for all those who want to make their way in the Church."
To this end, the church must open new doors and develop new pastoral attitudes, the cardinal said.
In his letter, he also reaffirmed the legitimacy of the Holy Year for people of different sexual orientations and their families.
This is due to take place in Rome at the beginning of September, but is not part of the Holy See's official programme.
Cobo commented: "In the context of the Jubilee Year, in which the Church opens its doors to those who are travelling together in hope, I hope that the event you have prepared will help to prepare you intensively to 'enter through the Holy Door' and that it will lead to a deeper encounter with Christ."