This is surprisingly difficult to answer. My own personal perspective sans data is that very few do. If social media is representative at all of chemists, then the fact that there are very few bloggers and tweeters on polymers compared to the number of chemists involved in those media supports my position. Also compare the size of their readership and/or followers. Further, look at how few polymer research articles are published in general chemistry journals such as JACS or Angewandte Chemie. Or how few polymer talks are given at the ACS national convention.
As I've said in the past,
"If you want to feel like an outcast chemist, take up polymer chemistry."Googling for an answer doesn't help much. Typing in the question outright doesn't provide any answer, so I took a different approach and searched on "X% of chemists work with polymers", and went with X from 10 to 110. (Yes, 110% since we all know that polymer chemists always give 110%. More on that in a minute.) The only hits I got were at 50% and 70% from the ACS and the University of Oregon respectively. Those numbers are preposterous. No citations are provided (not surprisingly).
I finally hit some real paydirt when I looked at the federal government's tabulations. The Bureau of Labor Statistic (BLS) has collected all the relevant data and provides an accurate picture (open up the spreadsheet for chemists if you to see all the details). In 2012, there were just under 88,000 chemists. Of that number, 2100 worked in "Resin, synthetic rubber, and artificial synthetic fibers and filaments manufacturing", 1900 worked in "Paint, coating, and adhesive manufacturing", and 600 in "Plastics and rubber products manufacturing". That's 4600 in manufacturing. There are some broader categories that undoubtedly include polymer chemists, such as the nearly 18,000 that work in "Scientific research and development services", and the 4600 that work in "Educational services; state, local, and private". Even if everyone of these last two groups were all polymer chemists, that would still only total to 27,200 chemists, not even 31% of the total workforce. I think a more realistic number would be just 10% of those last two groups, which would be 2260 more for a grand total of 6860 chemist. This is not quite 8% of the workforce.
Keep in mind that this is just "chemists". Chemical engineers, materials scientists etc. are not part of the numbers. It could be argued that the ACS pages includes a disclaimer:"As many as 50% of all chemists will work in polymer science in some capacity during their career."(emphasis added), but I'm not buying that either. Jumping fields and going into polymer chemistry is no more likely than an organiker becoming an analytical chemist or a computational chemist become a bench inorganic chemist. It can be done, but that is the exception, not the rule.
Also, it needs no mention that these are numbers for the US only but I would expect similar percentages for other countries. If some international readers have different numbers (or even anecdotes), please feel free to provide feedback either in the comments below or via email (address is on the upper left side of this page).
One final closing thought: If a mere 8% of chemists are able to provide the incredible bounty of polymers that the US and much of the world enjoys, I can't help but think that we are the James Brown of chemists - the hardest working people in chemistry!