Lesbian, Gay, Bisexual, or Transgender advocate

Case Analysis:  Jose, male 25 years old, wanted to get married to Paolo also male, 26 years old. They want to tie a knot before a judge who is a Lesbian, Gay, Bisexual, or Transgender advocate. Jose and Paolo believed that a priest will not allow them to get married because of their sexual orientation hence they want a civil wedding. If you are the judge, will you solemnize their marriage?

Why? Explain your answer based on law and family code. (Your opinion is baseless if it is not based on law.)