Iterator invalidation does not result in remote code execution in other languages. Regardless of what you call it (and you are in the minority by not considering that code UAF) the result is the same when combined with vtables and attacker-influenced heaps: arbitrary code execution.
shared_ptr is also not memory safe when combined with references, which you need to use to call methods on the shared_ptr'd object or to pass those objects to most functions.
In any case, a std::vector<shared_ptr<std::string> > would actually avoid the issue in this particular case.
Use after free... is more about use of raw pointers IMO. I wouldn't describe that code to be a "use after free" at all. In most languages, you are simply not allowed to change the container at all. Iterator invalidation is a hard issue in any language.