Given that passengers can be both men and women, I was expecting to find something like "die Fahrgastin" in the dictionary, but I can't find it.
Is there a reason for this, or is it simply an exception?
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As a rule of thumb, you are correct:
Most jobs or roles for people have a form denoting (biological) male or female individuals. Sometimes there are completely different words, e.g. Vater and Mutter, sometimes the female gets an "-in" attached (and sometimes an umlaut), e.g. Koch/Köchin. Typically, the male form is also the generic, gender-neutral form.
But yes, there are exceptions and with your "(Fahr)Gast", you found one of them.
And they come in all (gramatical) genders: Der Gast, das Opfer, die Leiche.
In all those cases, you depend on either context or a clarifying adjective to determine the biological gender.