I believe "They sell furniture here" should be accepted too.
This is indefinite-personal sentence. In indefinite-personal sentences, no pronoun is used, and the verb form is the 3rd person plural (i.e. it looks like a sentence with "they" dropped). Russian uses such sentences when the doer of action is unknown or unimportant, and therefore it's a good translation for the English passive voice.
But, of course, English uses "they" for unknown/unimportant speakers too (as in "they say"), so I believe this option should be accepted.
Both indefinite-personal sentences and reflexive verb are common. When talking about 'selling', there is little difference in meaning:
- В книжном магазине продаются карты. [reflexive verb, карты is the subject] means the same thing as
- В книжном магазине продают карты. [indefinite-personal sentence, it has no subject, the verb form is 3rd person plural]
- Тут продаётся мебель. [reflexive verb, мебель is the subject] means the same thing as
- Тут продают мебель. [indefinite-personal sentence, it has no subject, the verb form is 3rd person plural]
However, not all reflexive verbs can be used to convey a passive meaning. Generally, only imperfective verbs can be used this way. So, the imperfective покупаются 'are being sold' is OK, but the perfective купиться means something completely different ('to fall for some trick').
Interestingly, 'to sell' is an exception: the perfective verb продаться means 'to be sold (out)', which kinda works as a passive pair to прода́ть 'to sell'. But most verbs don't.
So, with most perfective verbs, you need to use an indefinite-personal sentence (or был(а) + passive participle, which is yet another construction with a passive meaning):
- Мебель продали. 'The furniture was sold.' [indefinite-personal sentence]
- Мебель продалась. 'The furniture was sold (out).' — this doesn't work for most perfective verbs, продаться is an exception [reflexive verb]
- Мебель была продана. 'The furniture was sold.' ['to be' + passive participle, this actually looks like English]
I don't think «Тут продаю́т ме́бель» would be used on a sign outside a shop. Just «Ме́бель» is much more likely, I think.