As the other person kind of pointed out, the specialists are doctors would be kind of a strange way of saying this. I actually typed the doctor's are specialists. I don't know where I would ever really say the specialist is a doctor. If I know that he is a specialist, then I would know that he is a doctor; how else could I know that he has a specialty?
A strange way of saying what? We're not given any context so it makes no sense to try and second-guess what the speaker is trying to say in a simple sentence like this. I'm sure someone could invent a context where the sentence would make perfect sense.
Duolingo is not a conversational course, it's a vocabulary and (to some extent) a grammar one, so you should be focusing on those aspects.
Almost all professions that end with the "ista" suffix do not change the ending. They are exceptions to the gender 'rule'. The definite article, however, typically does change gender depending on the gender of the actual person performing the profession. For example, "los especialistas" could be all male specialists, or a group of male and female specialists, but a group of female specialists would be "las especialistas."
That would be physicians. Doctor is a professional with that academic degree.
If you check this link it clearly indicates that las especialistas is commonly used despite what has been said. http://www.linguee.es/espanol-ingles/search?source=autoquery=las+especialistas Edited.. So I guess we can say in this instance they are talking about all male or mixed especialistas and if it were all female specialists we would use las especialistas.