I just heard a girl saying "Ella me cae gorda", but my male friends say "Ella me cayó gordo". Why did this girl said "gorda" en lugar de "gordo" if both were talking about a woman?
The grammatically correct way of saying it would be, as you supposed, Ella me cayó gorda. The DLE says so when defining the expression caer gordo, da a otra persona within the entry for gordo, da. That is, the grammatical gender of the adjective should match the gender of the subject. (This is irrespective of the gender of the speaker.)
I would say (and this is speculation) that your friends are using gordo even when the subject is feminine because they are reanalyzing the adjective as an adverb. This could be because the two most common expressions of this form (subject + dative + caer) employ adverbs:
- Ella me cae bien.
- Él me cayó mal.
Adverbs are invariable in gender and number. If gordo is being turned into an adverb, following the model of bien and mal, then it stands to reason that it won't change when the gender changes. Try listening carefully to what your friends say when the subject is plural (Ellos / Ellas me cayeron gord...).
This is not just a guess. In some dialects you can say, when you find someone or something disagreeable, Me cayó fatal. Normally fatal is an adjective, but in this expression it sometimes behaves like an adverb, so it doesn't change in number when the subject is plural:
- Los mariscos me caen fatal.
- Me caen fatal tus nuevos amigos.
Not everybody speaks like that (i.e. some people do say me caen fatales, using the "correct" plural form), but if you search online there are a lot of examples of fatal employed as an invariable adverb.
The same applies to horrible and probably a few others. So there's a pattern there.