C.S. Pearce rightly mocks some of the nonsense in Leviticus. It does not support her claim that the Bible may not be as virulently anti-gay as it seems, but it does bring into question why anyone should care. She also quotes a cleric who refers to the Bible's "core values of compassion, justice and peace." I don't know where she sees these core values in the Hebrew Bible; I see a lot of genocidal smiting.
These ancient writings have nothing useful to say to us today, except as warnings to ignore the proclamations of those who claim to speak with divine authority. If you want guidance on the morality of gay marriage, look at the equal protection clause of the 14th Amendment.
Pearce makes big claims about what the Bible does or doesn't say about homosexual practice. Pearce is not a Bible scholar; her background is in reporting. None of her arguments has anything to do with the correct reading of the biblical text in its literary and historical context.