"Hindu" atheism can be viewed as "Hindu" only if you interpret the word "Hindu" to include every thought current native to the subcontinent

But strictly speaking, atheistic materialism (even that of the Lokāyatas) is antagonistic to most principles of Hindu religion https://twitter.com/harshmadhusudan/status/1253547396446879746

There is a tendency to think the only fundamental difference between atheistic schools like Lokāyatas and "orthodox" Hinduism rests on the question of "belief" in a Personal God

That's not true. The differences are numerous

Lokāyatas / Charvākas reject Karma, re-birth, religious rites, varṇāshrama dharma

They show little to no interest in metaphysics. They are skeptical of "inferred" knowledge.

And they do not acknowledge the importance of the "invisible"

The obsession with "empiricism", the distaste for moral theorizing, distaste for philosophy in general, and a lack of enthusiasm for the "examined" life is what characterizes schools like that of Lokāyatas

This runs contrary to the predominant intellectual currents in India for the past 3000+ years that have ALWAYS emphasized the "invisible"

In that respect, the great Greek Socratic philosophers (be it Plato or Aristotle) are less distant to mainstream HIndu thought than Lokāyatas

Because Plato and Aristotle always acknowledged the "soul". And the importance of the Invisible.

Plato in his "Republic" engages in abstractions. In constructing "ideals"

That stems from a penchant for the "invisible" - which is in its roots a religious outlook

A pure materialist would never engage in abstractions the way Plato did

For a materialist, the only reality is the "observed" reality.

There is no room for imagination. For idealizations. For ordering of "values"

Not a surprise that Lokāyatas had a very relaxed attitude towards all kinds of sensual pleasures

Because in the materialist view, you can never honestly engage in moralizing and creating a hierarchy of values

As that is not based on the "observed" reality

It is not "objective" so to speak

In one of the Charvaka texts it is stated -

"The enjoyment of heaven lies in eating delicious food, keeping company of young women, using fine clothes, perfumes, garlands, sandal paste... while moksha is death which is cessation of life-breath..."

(Contd...)

"the wise therefore ought not to take pains on account of moksha.

A fool wears himself out by penances and fasts. Chastity and other such ordinances are laid down by clever weaklings"

This is rank hedonism.

Period.

The Charvaka authors are closer in spirit to Michel Foucault than any Hindu thinker in India.

Even several Christian theologians are less distant to us than Charvakas (though this may not go down well with parts of H-Right)

To side with Charvakas / Lokayatas is to not merely be un-Hindu, but it amounts to a rejection of moral philosophy, a rejection of the usefulness of "abstractions", a rejection of the "invisible", and a rejection of the "examined life"