One of the polls a while ago asked your opinion about this sentence:
Traditional and CONTEMPORARY furniture do not go well together.
But when we were discussing this sentence during a project meeting the other day, we couldn’t really work out what the problem is here. Can you help us please?
Bridging the Unbridgeable 
I’m no specialist, but for what it is worth, I think the sentence is correct. Maybe the (non)problem results from the fact that in e.g. “Red and green books do not go well together”, the noun is in plural while furniture doesn’t have one (normally). Therefore the verb is plural while the noun is singular in the example.
I think it’s perhaps the semantic change that’s the supposed problem. The original meaning of ‘contemporary’ was ‘belonging to the same period’ (e.g. if you were talking about the 19th c., ‘contemporary furniture’ would mean 19th c. furniture). The word has widened so that it now often means ‘modern’ (so ‘contemporary furniture’ means modern furniture). So, without context, it’s not quite clear what the sentence above means. But as with most of these cases, I think in real usage ‘contemporary’ is rarely ambiguous. Or perhaps usage writers have just not liked the semantic change of ‘contemporary’ because it moves away from its etymological origins.
The idea that we came up with is pretty much the same one that Kate Wild mentions. My problem with this sentence is that it is presented as a usage problem, while there is actually no problem at all. There are just different ways of interpreting this sentence according to the meaning one ascribes to ‘contemporary’. But more importantly, why would the association with the word ‘traditional’ in this sentence exclude the possibility of using ‘contemporary’ in one or any of its senses? Would we still see this as a ‘problem’ if they the sentence were as follows?
In other words, I don’t think that this sentence can ‘be’ wrong, especially when taken in isolation. But even in context, the meaning of ‘contemporary’ will usually be clear – as Kate Wild also points out.
However, we should remember that the survey from which this sentence was taken was held 40 years ago. It is possible that the semantic divergence of ‘contemporary’ has become more accepted. Talking about change, the OED gives the form ‘cotemporary’ as a variant during the 16th-18th centuries. Perhaps this form will be revived with the etymological original sense, while ‘contemporary’ becomes more associated with with the sense ‘modern’ or ‘up to date’.
I really don’t see the issue here either, as an adjective the word contemporary is described as belonging to the present whereas traditional is something described as being long-established. The two can sit happily together and are actually often used together to describe a furniture style that combines the two. In your post you say you conducted a poll but don’t say what the results of this poll were? Could you enlighten us please, just out of self interest, as it would be interesting to know what others opinions are.