A redesign of FamilySearch is in the works to provide records of same-sex couples by 2019.
In 2015, FamilySearch stated that they would be adding a feature for same-sex relationships in the future. The goal of FamilySearch is to "capture, store and provide records and an accurate genealogy that represents the past, present and future families of the world," according to a statement on their website which was updated in April 2018.
FamilySearch is owned by the Church. See the full statement below:
“The goal of FamilySearch.org is to capture, store, and provide records and an accurate genealogy that represents past, present, and future families of the world. To support this goal, same-sex relationships, including same-sex parents and same-sex couples, will be provided in FamilySearch Family Tree. Several systems that surround Family Tree, such as tree and record searching, must be significantly redesigned to support same-sex relationships before Family Tree can release this capability. We expect to finish this work by 2019. Following this work, the FamilySearch Family Tree application can then allow same-sex information to be recorded. We appreciate your patience and desire to preserve the world’s genealogy in Family Tree.”