The ideologue is basically right. But in biology there are no rules, only regularities, and evolution tends to explore every conceivable exception to those regularities. Some exceptions are fatal or don’t reproduce effectively, but that doesn’t stop them from spontaneously reappearing. You can just read the Wikipedia articles on sex determination and see most of the exceptional situations.
I deal with fungi, which is a kingdom where many of the most spectacular deviations from M/F appear. Species with over 200 sexes, clonal species with effectively no sexes, and species where cells are two compatible sexes at the same time and can go through the whole sexual chromosomal routine all by themselves.
I don’t like how he goes "the exception proves the rule’. What rule?
That apparently X & Y chromosomes are the most important factor in sex determination? There are genes on the other chromosomes that act as effect modifiers.