Don't forget Illusory Reality's limitations
... you can choose one inanimate, nonmagical object that is part of the illusion and make that object real.
Is a corpse an 'inanimate object'? Is it really a corpse if it was never alive in the first place? These are interesting philosophical questions, but as a practical matter, when you Animate Dead something, they all become moot. Casting the spell settles the matter. I mean, it's right there in the name: Animate Dead.
An undead creature is neither an inanimate object, nor "nonmagical." The act of casting Animate Dead causes the object to immediately cease to be a valid target for Illusory Reality. In turn, that means Animate Dead itself no longer has a valid target, meaning it can't work.
In other words, Animate Dead causes itself to fail to activate, which causes it to be a valid action, which causes it to fail to activate. This is exactly the same as the grandfather paradox. Which is just another way of saying "you can't do it".
The object can't deal damage or otherwise directly harm anyone.
The text of the two abilities is in conflict. So which one is more specific?
From one point of view, Illusory Reality is. Animate Dead works on any corpse or pile of bones, but the half-real ones created via the illusion are special. In which case, this restriction trumps Animate Dead, and since a zombie or skeleton can do these things, you can't turn the "corpse" into one. That's all the necromancy can do, it can't create half-skeleton-like things that obey the restriction. This would mean the spell must fail entirely.
From another, Animate Dead is. Illusory Reality's rule about 'no damage' is a general rule, but Animate Dead adds new magic and changes the scenario. Animate Dead would thus overrule this restriction.
However, if the second interpretation is correct, many other sort of weird and silly loopholes are also possible. For example, I could create a burning torch, then use it to set something that IS real on fire (just as long as I don't try to damage someone with it directly). I could create pebbles and then cast Magic Stone on them. Or boulders, and then cast Catapault on them. This would make a mockery of the idea that the objects can't do damage.
The most reasonable interpretation to me is the first one. Illusory Reality trumps Animate Dead, the object isn't real enough to "deal damage or directly harm anyone", and that's essentially a prerequisite for Animate Dead to be able to target it.