Is there a way to make member function NOT callable from constructor?

I am afraid the answer is "no, it's not possible to protect against this at compile-time." It's always difficult to prove a negative, but consider this: if it was possible to protect a function this way, it would probably have been done for weak_from_this and shared_from_this in the standard library itself.

No there is no way. Consider:

void call_me(struct widget*);

struct widget : std::enable_shared_from_this<widget> {
    widget() {
        call_me(this);
    }

    void display() {
        shared_from_this();
    }
};

// later:

void call_me(widget* w) {
    w->display(); // crash
}

The thing is there is a reason you want to check for not calling shared_from_this in the constructor. Think about that reason. It's not that shared_from_this cannot be called, it's because it's return value has no way of being assigned yet. It is also not because it will never be assigned. It's because it will be assigned later in the execution of the code. Order of operation is a runtime property of your program. You cannot assert at compile time for order of operation, which is done at runtime.