This is similar to this question, but the other way around.
How does Malleable Illusion interact with an illusory object made real by Illusory Reality?
For example, if I make a silent image of a sword and then make the sword real with Illusory Reality, what happens when I try to use Malleable Illusion during the minute of reality, perhaps to change the sword into a lump of coal?
This is the fun part of being a high level illusionist: you're essentially a reality warper. There is no contradiction between Malleable Illusions and Illusory Reality. The first one allows you to change the nature of the illusion (as long as it fits within the normal parameters of the spell), while the second one allows you to make one inanimate object in that illusion real.
The crux of this is you must consider the sword made real by Illusory Reality as still part of the illusion, so that it can be morphed by Malleable Illusion. In other words, the real sword must also be illusory.
And yes, real things can be illusory in D&D. Consider the creation spell. It is from the Illusion school, and is able to create anything from vegetable matter to mithral. It is composed of the same stuff as the illusions in Illusory Reality:
Creation
You pull wisps of shadow material from the Shadowfell to create a nonliving object of vegetable matter [...]
Illusory Reality
By 14th level, you have learned the secret of weaving shadow magic into your illusions to give them a semi-reality.
Note that anything you create with creation can actually be morphed by Malleable Illusion, because creation fits the requirements of Malleable Illusion.
It stands to reason things made real by Illusory Reality can be altered by Malleable Illusions as well.
Both class features, MI and IR, are part of the same Wizard school. They should be complimentary and not exclusive. That is, what point would there be in a Wizard losing access to one ability (MI) by applying another (IR)?
The heart of the illusion school is tricking other people. Imagine how fun/cool it would be to hand someone a sword and, 6 seconds in to the battle, watch as that sword becomes a lump of coal? As a player who plays an illusionist, stuff like that is incredibly satisfying because it gets to the core of what that school represents.
The two class features do not contradict each other. An illusion spell which creates real objects is subject to MI in the same way purely sensory illusions are. It is cooler to allow it than to restrict it.
So, yes, MI can interact with an object made real by IR.
From the description of Malleable Illusion:
...you can use your action to change the nature of that illusion ... provided you can see the illusion. (PHB 118).
Emphasis mine.
Now, from Illusory Reality:
... you can choose one inanimate, nonmagical object that is part of the illusion and make that object real... The object remains real for 1 minute. (PHB 118)
Once again emphasis mine. The way I read it, an illusion made real by Illusory Reality temporarily loses the property of being an illusion. Note the difference in wording between Illusory Reality and a spell which creates tactile illusions such as Mirage Arcane
The illusion includes audible, visual, tactile, and olfactory elements... so while the creature is aware of the illusion's presence, the creature can still physically interact with the illusion. (PHB 260)
Based on this, I believe there is a distinction between an illusion with tactile properties and real objects. The former can be effected by Malleable Illusion, the latter cannot. And based on the wording, Illusory Reality appears to create the latter.
When you use Illusory reality, the thing you affect ceases to be an illusion and thus will not work with Malleable Illusion.
Illusory Reality says:
When you cast an illusion spell of 1st level or higher, you can choose one inanimate, nonmagical object that is part of the illusion and make that object real.
The spell text states that the object you choose starts as an illusory object but then becomes a real object. The way it is phrased and the way they are explicitly contrasted in the sentence make it clear that the object is not now illusory and real, just real.
More evidence that Illusory Reality creates real things and not some partially real thing that can be interacted with by illusions is this conversation by Jeremy Crawford:
@BrailSays: lvl 14 illusory reality+illusion of adamantine wall, incoming siege boulder/ballista. What happens?
@JeremyECrawford: It could hit the wall.
@BrailSays: wall hp? no damage ?
@JeremyECrawford: The wall is real, so the DM would treat it like any other wall.
No illusory object can stop or take damage from a projectile without explicitly saying so in its spell effect. This new, non-illusory wall has HP and AC and all the other properties of a real wall because it is real. It has none of the properties of an illusion because it is no longer one.
D&D often depends on using the plain english meaning of words. Neither illusion or "real" have any concrete game definition.
Illusion is defined as "something that deceives by producing a false or misleading impression of reality.". And illusory is defined as "based on illusion; not real."
Real is defined as "being an actual thing; having objective existence; not imaginary".
Thus, it is apparent that something cannot be illusory and real simultaneously.
So, when you use Illusory Reality to turn part of an illusion into an object, it is no longer an illusion. It is a real thing. Thus, you will not be able to apply Malleable Illusion to it because Malleable Illusion only works on illusions and not objects.
To apply this to an example you used: the sword you made started as an illusion and then became a real sword. Unfortunately, Malleable Illusion does not work on real swords. It doesn't work on the one the barbarian bought in a shop and it doesn't work on the one that was formerly an illusion. Unfortunately, you'll just have to wait until Christmas to get your coal ;-).
