@tkoch!220 (merged) is about thread safety of the cache not the shape functions themselves. I guess to understand the problem one needs to know more details on what is actually meant here.
Personally I never encountered problems with thread safety for parallel assembly in dune-fufem, because (in dune-fufem) all LFEs, LFECaches and shape function caches are thread-local.
On the meeting we agreed that a single LFE does not need to be thread-safe. However, we would like to guarantee that there's no race conditions between separate copies of the same LFE. @santiago.ospina and @carsten.graeser will take care for documenting this.
Grepping through dune-localfunctions it seems that the (former) generic LFE implementations use shared_ptss which may violate the above given guarantee. @robert.kloefkorn want's to have a look at this.