Is insisting on calling “consciousness” a real thing appropriate?

It appears the Lord Buddha criticized natthikavādaṃ (moral nihilism) because it is doctrine based on grasping (upadana). In other words, the Lord Buddha appeared to not criticize natthikavādaṃ because of disbelief in an afterlife.

In Buddhism, the word "grasping" is "upadana", which means to "take something as one's own". Due to views of "self" or "ego", selfishness arises. Selfishness leads to moral nihilism -- the mind is grasping at dirty animal lust as "me" and "mine" and "I". This dirty grasping at dirty things, leading to harm & trauma of everyone involved, is natthikavādaṃ.

For minds out of touch with reality, some suttas about "grasping" and "selfishness" are as follows:

Now, craving is dependent on feeling, seeking is dependent on craving, acquisition is dependent on seeking, ascertainment is dependent on acquisition, desire and passion is dependent on ascertainment, attachment is dependent on desire and passion, possessiveness is dependent on attachment, stinginess is dependent on possessiveness, defensiveness is dependent on stinginess, and because of defensiveness, dependent on defensiveness, various evil, unskillful phenomena come into play: the taking up of sticks and knives; conflicts, quarrels, and disputes; accusations, divisive speech, and lies.

DN 15

But viewing consciousness as "cognition" is not "grasping". This is why the Lord Buddha said the reality of consciousness is that is cognises.

The question asked makes no sense because the question seems to irrationally believe the idea of a "thing" is the arising of "self" or "grasping"; such as to view a computer as a "computer" is "grasping".

The Lord Buddha did not to teach to abandon the idea of "things". What the Buddha taught to abandon is described below:

16. "But, monks, there is here a well-instructed noble disciple who has regard for Noble Ones, who knows their teaching and is well trained in it; who has regard for men of worth, who knows their teaching and is well trained in it: he does not consider corporeality in this way: 'This is mine, this I am, this is my self'; he does not consider feeling... perception... mental formations in this way: 'This is mine, this I am, this is my self'; and what is seen, heard, sensed, and thought; what is encountered, sought, pursued in mind, this also he does not consider in this way: 'This is mine, this I am, this is my self'; and also this ground for views (holding): 'The universe is the Self. That I shall be after death; permanent, stable, eternal, immutable, eternally the same shall I abide in that very condition' — that (view), too, he does not consider thus: 'This is mine, this I am, this is my self.'

MN 22

In conclusion, insisting on consciousness as an objective real thing does not inherently lead to unethical behavior (moral nihilism) just as the Buddha warned. Only insisting that consciousness is "self" or "me" or "my" inherently leads to unethical behavior (moral nihilism) just as the Buddha warned.

Theravada Buddhist answer.

Is insisting on calling “consciousness” a real thing appropriate?

It is not.

Consciousness (Citta) exists only as a taker of objects. If one has to characterize it as anything, it is rather a "knowing, cognizing or processing" of an object and not a real thing.

Here is a quote (my highlights) on the nature of Consciousness from the book "Comprehensive Manual of Abhidhamma", by Ven. Bhikkhu Bodhi:

"Consciousness: The first chapter of the Abhidhammattha Sangaha is devoted to an examination of citta, consciousness or mind, the first of the four ultimate realities. Consciousness is taken up for study first because the focus of the Buddhist analysis of reality is experience, and consciousness is the principal element in experience, that which constitutes the knowing or awareness of an object.

The Pali word citta is derived from the verbal root citi, to cognize, to know. The commentators define citta in three ways: as agent, as instrument, and as activity. As the agent, citta is that which cognizes an object (arammanam cinteti ti cittam). As the instrument, citta is that by means of which the accompanying mental factors cognize the object (etena cintenti ti cittam). As an activity, citta is itself nothing other than the process of cognizing the object (cintanamattam cittam).

The third definition, in terms of sheer activity, is regarded as the most adequate of the three: that is, citta is fundamentally an activity or process of cognizing or knowing an object. It is not an agent or instrument possessing actual being in itself apart from the activity of cognizing. The definitions in terms of agent and instrument are proposed to refute the wrong view of those who hold that a permanent self or ego is the agent and instrument of cognition".

-- Comprehensive Manual of Abhidhamma, Chapter 1: Compendium of Consciousness, Guide to §3, p. 27.