How To Access Other Class Instance Variable Inside A Static Function

You've got a static function. How are you going to access member variables? Either make the variable static or the function non-static.

A static member function is related to the class, not to any instance of that class. It's pretty much like a global function that's been declared a friend of the class (with a kind of odd name that includes the class name tacked on the front).

Bottom line: to access (non-static) data, you need to specify an instance of the class whose data it's going to work with (just like you would with a friend function).

Instead of making IsValid a global function (which you've accidentally done here) or a member function (which I'm sure was your true intent), make it a functor, and in the functor's constructor pass the instance you want to use.

Like this:

class ClassA
{
    private:

    UtilityClass utilityCls; // this is the instance that I need to access

    virtual void Read();

  struct IsValid : public std::unary_function<char, bool>
  {
    IsValid(UtilityClass& utility) : utility_(utility) {};
    bool operator()(char c) const 
    {
      return utility_.ProcessData(c);
    }
  };
};

Use it like so:

void ClassA::Read()
{
    ....
    string str = "abcdefg"; // sample only
    if(find_if(str.begin(), str.end(), IsValid(utilityCls)) == str.end())
    {
        ....
    }
}

Static functions of a class are really meta-functions: functions which are of use to the class as a whole, but not to any particular object of the class. Thus they don't have any way to access the members of a particular object, in particular they're missing the implied this pointer that most member functions contain.

If you need a static class to have access to an object's members, you must explicitly pass a pointer or reference to the object. Usually it's better to make the function non-static.

P.S. Your definition of IsValid is incorrect, it should be inline bool ClassA::IsValid(char c).

You can't access an instance variable without first creating an instance of the class. Either make IsValid non static or add code to your static method like

Class a; a.utilityCls.ProcessData();