Iterating over vector in one thread while other may potentially change reference

I have a vector allow_list that is periodically updated in a thread while another serves a function that checks if a certain string is in that allow_list via:

if (std::find(allow_list->begin(), allow_list->end(), target_string) != allow_list->end()){
    allow = true;
}

Now, the other thread may do something like this

// Some operation to a vector called allow_list_updated
allow_list = allow_list_updated;

Should I add a mutex here to lock and unlock before and after these operations? My intuition tells me it's "ok" and shouldn't crash and burn but this seems like undefined behavior to me.