The solution is two-folded. First of all, there is a known issue described on the Sitecore Knowledge Base. The remedy is to download the support dll and to make changes to some WFFM files and items. Make sure you pick the right Sitecore version.
But even after applying that fix, I still ran into the same issue. It turned out that Sitecore WFFM MVC relies on the default dependency resolver and that I've set that resolver according to the Autofac documentation as follows:
var builder = new ContainerBuilder();
// Register your types
// ...
var container = builder.Build();
// Set the resolver to Autofac
DependencyResolver.SetResolver(new AutofacDependencyResolver(container));
WFFM expects to find the Sitecore dependency resolver there, but finds Autofac instead. A resolver that doesn't know anything about the WFFM types. To overcome that issue, you must register the WFFM types yourself.
// Sitecore WFFM
builder.RegisterType<Sitecore.Forms.Mvc.Controllers.ModelBinders.FieldBinders.DefaultFieldValueBinder>().AsSelf();
builder.RegisterType<Sitecore.Forms.Mvc.Controllers.ModelBinders.FieldBinders.CaptchaFieldBinder>().AsSelf();
builder.RegisterType<Sitecore.Forms.Mvc.Controllers.ModelBinders.FieldBinders.CheckboxFieldValueBinder>().AsSelf();
builder.RegisterType<Sitecore.Forms.Mvc.Controllers.ModelBinders.FieldBinders.DatePickerFieldValueBinder>().AsSelf();
builder.RegisterType<Sitecore.Forms.Mvc.Controllers.ModelBinders.FieldBinders.ListFieldValueBinder>().AsSelf();
After that, data from list fields should be saved properly again!