Hi BuffettNH 
First of all you will have to seperate these two concepts from each other, since they can easily stand on their own. 
ICM ALWAYS matters. The deeper you are (the bigger the bubble factor) the more important it gets. But even in your first hand in a tournament ICM is present and influences your results. For the most time you can just ignore it because factors like future game compensate the effect, but it's still there...
Nash is a different concept that is based on the nash equilibrium. Fundamentally it states that, as long as you base your decisions on the equilibrium, you can not be exploited and therefore there is no possible way for your opponent to play +EV against your style. At the same time, as soon as he doesn't play according to Nash himself, you gain profit.
Of course, both concepts are often used together and fit very well, but they are still different concepts.
To answer your question:
You can not decide on not using ICM. The concept itself won't go away just because you ignore it. The question is not "When do I not use it?", but "How do I take it into account?" or "How important is it in my current situation?".
Talking about Nash your assumption is not entirely wrong. There is a possible szenario where a "wrong" call from your opponent will cost you money. The concept itself is still true though, since he will loose even more. The only players that gain are the ones that are not playing the hand. Therefore it can make sense to adjust your ranges and differ from the standard Nash ranges. This makes even more sense, because Nash is not maxEV. It's just not -EV against a single opponent. If you want to play a hand maxEV you will have to adjust according to your opponents behaviour.
It's obviously hard to give you some general advice on how to adjust to your opponents since it depends on the situation. There are too many different szenarios. It won't be possible to cover them all obv.
My advice would be to always think before you act. Just because Nash suggests to push the push is not perfect immediatly. Always think about the alternatives and try to be aware of what you are doing and why.
If you have furhter questions feel free to ask!
Regards,
Asaban