Ethical Problem

Utilitarianism's Solution

Homosexuality: is it wrong to love and marry the same sex?

As Utilitarianism doesn't reference the Bible or any other holy book, or even religion in general, there is no religious background in utilitarianism for why homosexuality is wrong.
Being with the person you love is probably one of the largest, most important instances of promoting pleasure and mitigating pain.
The act of being married in itself causes no pain to anyone. Mill says that we need to harmonize with the ends of others, promoting the good in society. Being in love brings happiness and mitigation of pain; so, according to utilitarianism, there should be nothing wrong with homosexuality at all.