You asked: "If the Urantia movement were to have churches or temples, would same-sex weddings be performed by the Urantia clergy, in your opinion?"
Thanks so much for this interesting question to us here at TruthBook.
I suspect that in asking this question, you already have a bias, one way or the other, so my reply may or may not be helpful...
I don't believe there are any teachings in The Urantia Book that give either approval or disapproval regarding homosexual relationships, much less same-sex marriage, and I do not have an opinion on how anyone will use the information in The Urantia Book to formulate their personal position on this matter.
Having said that, I have to add: with any luck, the Urantia movement will not develop any churches or temples using that name.
The Urantia Book is not a religion. It is not a church. It is a book of vital information for the spiritual advancement of the entire planet-information that can improve the religious experience of practitioners of ALL religions and even those with NO particular religion.
If you are a reader/student of the teachings, you will be aware that The Urantia Book does not espouse institutionalized religion, as such, nor do its teachings promote clergy - priests or other "middle-men" who stand between man and God. Instead, it fosters the religion of personal spiritual experience - one's own brand of "religion," unique to each individual and that individual's relationship with the personal heavenly Father who indwells his/her mind. Of course, this does not mean that there will not be attempts to start churches which DO foster those ideals; and I know that there have been attempts in the past. I do not know of any successful efforts to date, but then, I don't know everything :)
What I HAVE seen happening is that inspired readers/students/leaders have taken it upon themselves to become ordained in one way or another. It is these pioneers who are in a great position to carry the teachings through just the kind of situations that you are asking about: performing life's milestone ceremonies, such as marriage, baptism and funerals. But, far from being "clergy" of the Urantia movement (which again, is not a church or religion - there is no official clergy), these ministers would, in most likelihood, work from within an already established church or religious group to seed the good news, "Urantia-style."
As for whether such a person would be willing to perform same-sex marriages, I guess that would have to be the determination of the minister and of the particular group association. And again, I can't predict behaviors.
All I can say is that I hope that any minister who wants to promote Urantia Book ideals will study carefully the religious life of the Master. Although he never mentioned same-sex marriage, It seems to me that when we look to Jesus' life, what we see most is his loving nature, his tolerance and forbearance, his friendliness and his compassion.
Jesus made it clear that marriage between man and woman was the highest kind of relationship, as it is that union that can produce new souls into the world and create the ideal family unit. At the same time he promoted love as the "greatest thing in the world." And when he did make pronouncements, they were against "pride, cruelty, oppression, and hypocrisy."
Again, Jesus' highest ideal, and the way he lived his life, was Love ... the true love of God can be shared between diverse pairings of people, and that kind of love is an eternal reality worthy of recognition if the participants so wish.
So, I've ended up giving you my own personal thoughts on this matter, but again, there are no Urantia Book teachings about this specific subject of same-sex marriage. And - I am not a minister, nor in a position to perform marriages. It's just how I feel personally.
Thanks again for writing - it's a timely question. I hope that my reply has been helpful.