This is a very controversial question. There are those who think that such relationships harm society and there are others who think that the relationships themselves do not have much effect on society and that allowing them makes our society a better place.
People who are socially liberal tend to believe that same-sex relationships per se do not have an influence on society. They argue that same-sex relationships are essentially the same as heterosexual relationships. Both are simply ways of allowing people to fulfill their needs for love and companionship. Liberals would tend to believe that our society benefits from allowing such relationships to have legal status and to be accepted. When we do this, they would say, we make our society more tolerant and more just.
By contrast, people who are socially conservative believe that same-sex relationships have a negative effect on society. Most typically, such people believe that same-sex relationships tend to devalue heterosexual relationships and undermine the importance and sanctity of marriage. They argue that marriage is an extremely important institution in our society because it provides for stable families and a better environment for children to grow up in. By allowing same-sex relationships, conservatives say, we are harming our society and reducing the extent to which we have respect for the institution of marriage.
There is no way to know for sure which of these points of view is correct. It is a matter of opinion and we must all decide for ourselves what we believe.