I have not done a lot of experimenting with neo. magnets but I would definitely expect the bad effects of iron to be much less in neo. magnets. I have two neo. magnets right in front of me right now and I can push both north poles together and hold them without a great deal of effort. So that leads me to believe that the magnetic dipoles in the magnets to rotate around as in a normal magnet. If they didn't I wouldn't be able to hold them together.
Well.
Are the Neo magnets really small?
They can't apply a force strong enough to counter the force you applied. That's why I believe you can force the opposite poles together... I HIGHLY doubt that is possible with stronger magnets. Actually I'm quite sure that would not happen.
I can do the exact same thing with tiny Neo magnets.
But I could not do the same with ones a little bit larger.
Another explanation is that the magnet's field is weaker than what it was before... That is another thing.
Now when I think about it, the effect that happens when the magnet is attracted should be equal when the magnet is repelled. Because their atomic structure and dipoles are always equal.
When I used an electromagnet I believe it will attract/repel the Neo magnet equally the same.
If not, this effect should be present when playing around with magnet alone.
In terms of iron based magnets I'm not sure...