Sure, there may be a maximal element, but not necessarily a maximum (there might be multiple people of equal and maximal gayness, not just one person).
Also, not relevent to the logic here per se, but last time this went around the conclusion was that a spectrum implies a total order, not just partial.
I don’t know much about this, but I can’t help but think that “complete” and “consistent” are doing a lot more work in that sentence than my current understanding of the terms would lead me to believe.