Except that 'professional' is not a job; it is an adjective which can describe the level of expertise of a person or company at any particular job. No one ever said 'What do you do for a living?' "I'm a professional." Everyone present would be waiting for the noun which would tell them what you actually do, and perhaps would wonder if you'd had a stroke mid-sentence.
We do not have enough context here. As an adjective "professional" means "We are of high quality."
As a noun it's the object of the sentence and can be pluralized: professionnels/professoionnelles"—we are professionals, we're lawyers, doctors, teachers, prostitutes, etc.
Duolingo gives us no indication which it wants. Therefore, I'd say the plural should be accepted.
Now, my argument could fail if "professionnel" itself is not like the noms de profession avec être and drops the indefinite article ("nous sommes avocats" etc.): "Nous sommes des professionnels" or "Nous sommes professionnels"?
If the latter, Duolingo needs to work on this question and accept "We are professionals."
Your comment makes no sense - you mention latterly the possibility that 'professional' is not like noms de profession and does not drop the indefinite article, then say that if this is the case, Duo should accept the plural. In fact in the case you state, Duo should not accept the plural, and this is in fact the case. Larousse does not allow this inference, except in the case of the feminine 'professionnelles', which it lists as a polite term for a prostitute, but even then would unlikely be the word a prostitute would use to describe herself. All other uses of 'professionnel' requires additional words to describe what you are a professionnel of, eg, 'Je suis un professionnel de la boxe', and even then it requires an article to make it a noun. It's an adjective here; the acceptable answer is 'We are professional'.
Google translate "Nous sommes professionnels" as "We are professionals" and "professionnel" is also a noun in French. Can anyone explain why the Google translation is not correct? I did report that the answer "We are professionals" should be accepted since at the moment of writing this comment it is not accepted.
As an interesting side note, Google translates "Nous sommes les professionnels" as "We are professional." Of course, duolingo exists because you can't yet trust automatic translations, but can anyone explain why this translation is in fact wrong, if it is?
Google Translate invites users to input "improvements" to its so-called translations. Anyone -- and I mean anyone -- can put something in there. It does not mean it is correct. It is crowd-sourced. Duolingo takes input from users but it is first vetted. People can present their rationale, their justification, their sources, and have the opportunity to engage in a meaningful dialog. Unless Duo's resident francophones will vouch for the results you obtained from GT, they will have to go down as violating all the principles that Duo has been teaching on this site.