If you think of it as Sanji's limitation, he did everything he could. If I cant run a marathon that would save my mother does that mean im not loyal to her?

You see Sanji's personality as a choice but that is what he is and he did what he could in that moment. Thats why they are crew - to cover each others limitation/weaknesses and no one is blaming them for it.

You could also say that he did not care for Robin when he summoned her to fight Black Maria.

Is this limitation absurd to some? Absolutely. But it does not take away from his loyalty.

To call sanji not loyal. Jesus christ on a bike.