So then people come out to their family and friends, many of which will accept them (despite some who won't/don't). Then, even if they are against same sex couples getting married prior to their loved one coming out, they will likely grow to support seeing their loved one happy, particularly if they see them in a loving, committed relationship. Then those loved ones will start to share their experiences and support for their loved ones with people they know and who likely respect their feelings, who then start to see where others are coming from.
It is much more difficult to see the other side on this issue because in reality the lives of those who are against same sex couples getting married are not affected by same sex couples getting married, not in a measurable way. It is nothing more than their beliefs being offended, which is something that they do not have a right not to have happen.