Both answers are always correct
The extreme ends of a spectrum are always correct to some degree because they are co-dependent, left can't exist without right and right can't exist without left. This means at one level of relativity gender is a spectrum because it is a consequence of the distributions of hormones inside the body, the gradient of energy that makes up the physical form is infinite, which means that the composition of someone's biochemistry is always going to be on an spectrum that converges towards infinity over time, however at the same time there is a distinction between man and woman because physical form can't exist without distinction, this will create a relative polarity which is the relationship between men and women, the interaction of this polarity creates an endless growth of information which is the essence of spacetime, so you can't have man without women, and their physical representation is a polarity, a binary distinction between genders, however the spectrum of sexuality is infinite by nature, otherwise the gradient that connects the relativistic polarity wouldn't exist.
So sexuality is a spectrum because it is a consequence of a gradient of distributions of hormones which are going to be determined by the genetic distribution of biochemistry (DNA) of a social structure, but at the same time by definition gender is binary because the definition of matter in spacetime is a distinction/polarity which is the nature of geometry.
Conclusion
So both perspectives are correct at the same time, the way someone feels about them is a projection of what their biochemistry is aligned with, straight people can't exist without transgeder or homosexual people, because someones sexual orientation is a byproduct of the spectrum of energy which is a symmetry by nature, masculine and feminine, depending on someone's biochemistry composition they are going to exhibit behaviors that are more masculine or feminine or both depending on the situation, but the physical representation of their energetic balance is going to be a polarity because otherwise the boundary between masculine and feminine wouldn't exist. Geometry by definition is distinction, and distinction is polarity, so the spectrum of sexuality is infinite and always convergent towards a relativistic multifractal symmetry, but at the same time the physical representation of masculine and feminine is a polarity because that is what defines geometry in spacetime.