Using ellipsis, the sentence (fragment) could be, "Exactly as the others [do]." Generally, as goes before a clause with a noun and verb, while like goes with anything else. Assuming the elided word do, as works well here. In actual usage, like and as aren't used with such a precise distinction; this is another reason why as is reasonable here. I am a native English speaker, too. Both options sound fine to me.
When the gender of the antecedent is exclusively feminine, then las otras is correct. When the antecedent is exclusively masculine or is of mixed gender, then you would say los otros. We don't know from the example what the plural noun is that is being referenced here, but we can assume, from the forms selected, that it must be plural and feminine in gender.
Your statement is not completely correct. If we assume that the authors of this course understand Spanish grammar, then we must assume that the sentence is correct as it has been written, and that this mysterious context should it ever be revealed to us must include an antecedent for this pro-noun that is both plural and feminine.
curious doesn't the sentence imply feminine here. (exactly like the other girls) If it wasn't implying just girls shouldn't it have read Los otras? or does does it require (las) because otras begins with an o. Having the most trouble figuring all the masculine and feminine nuances of Spanish. Still need to watch more you tubes on that subject.
"Exactly as the others" may sound odd on it's own but it carries the meaning of the Spanish phrase just fine. And the fact that so many native English speakers thought it was a reasonable translation indicates that it should be accepted. I don't want to learn to talk like a grammar textbook, I want to communicate