The risks increase with every new OS update; I really really really would not want to support anyone still on FM10 and 11 on Sierra at this point.
I actually had to work in FileMaker 11 using Sierra just yesterday, and oddly enough it actually behaved much better in Sierra than it did in El Capitan!!
In El Capitan there were loads of graphic glitches when trying to move layout objects around etc... However, in Sierra, worked just fine...
Having said that I really wouldn't run a live production, business critical system in that configuration and instead would try to get the FileMaker system upgraded to v15 for use with Sierra...
So far I haven't seen any flaws with FM11. It's even running better than under El Capitan, no black screen anymore in the graph when moving TOs. But I'd test the clients solutions thoroughly though.
Unfortunately we don't always have a choice as we have to deal with client choices. I even have a client I work with a few times a year that still insists on using FM 8.5. I have to do that using Win 7 in Virtualbox.
@skywillmott & @okramis
Glad to hear that the graphic glitches seem to be better. I'm sure you know that we can't always force the clients into upgrading. For the ones that I'm supporting they are actually running on Windows 7 and aren't looking to upgrade their OS or Filemaker. C'est la vie.
FM Pro Advanced 11.0.4 crashed after printing to a PDF under Sierra 10.12.1 beta
I've just tried printing to PDF from FM Advanced 11.0.4/Sierra with no problems. Perhaps this was fixed in the release version of OSX 10.12 or is the result of some other FM/PDF issue (which are not uncommon).
I agree with others that FM 11 Sierra is working much better than with El Capitan.
Regarding clients upgrading, I have a client who bought FileMaker Server 5 and clients (Windows), 15 years ago, and have stayed with it ever since, despite my periodic suggestion that they might upgrade. From their point of view, it does what they want, is exceptionally robust - and they've saved a lot of money from not upgrading. Who is to say they're wrong? Not me.
You ultimately are a consultant providing advice, you can't make them take the advice. But before brushing them off, I would ask them if they have considered ramifications of corrupting their data or it getting hacked and to realize that a developer can't "fix" all things that go wrong. This is not the 1990's where being cavalier about security has minimal risk. Businesses go out of business for having information hacked or end up in court spending lots of money on lawyers, etc. I also tend to find companies that won't keep current on software are also often pirating software, which is another vulnerability. The question I ask such clients is whether they are building a business to survive this month or do they want to be in business years from now? It's about like saying I trust the area my office is in, so I'm not going to waste money buying a lock for the front door. Getting too cheap can cost you a lot of money down the road.
Also, giving them fair warning about vulnerabilities takes some of the responsibility off of your shoulders in providing consulting to them in that if there is a failure, you can say they did not follow your advice to begin with. And I would put your advice and warnings in writing, or at least in an email that you save.