Yeah, think about all the stylish Italian dudes who you've seen wearing shantung ties. Were they ever wearing them with flannel/in winter, or always with linen/in spring/summer? It's perhaps an anachronistic association but one that ultimately makes sense, I think. It's a more loosely woven tie, with the imperfections/slubs lending themselves well to the casual, rumpled look of a linen jacket.
I go back and forth on this. WOn't claim any authority about this matter, but while I understand there is a tradition, what strikes me more about the slubbiness of Shantung is the casualness of it rather than the summeryness of it. Some nice Shantung's are available from Conrad Wu (pretty slubby, so a matter of preference...some might think too slubby). They are substantial ties in a sense, not heavy, but dry and stiff. I'm probably going to wear them more in the spring/summer (they do feel more appropriate for that season), but the olive one I would happily wear now when I'm in a more casual mood.
The tie in my pic a few pages back is a denim/linen. I like the texture in it, and it's a substantial tie: heavy and thick fabric. Feels late summer/early fall, but again, wore it today (late January). Just wanted a navy tie with some texture.
So, seasonal appropriateness is a factor I play with, a strong constraint, but not a deal breaker. In the context of a set of fits, a heavy linen mixed with some wool ties over the course of a week seems, in that context, ok.
Edit: Shucks Butch, really?