The subject is self-explanatory. But let me expound on it a bit.

First, a little bit about Hinduism : This label did not exist prior to Islamic arrival into Indian subcontinent. If one goes back beyond 1200 years, there is ZERO reference to 'hinduism'. Not even Indians themselves used the word.
Indian schools of thought were just as diverse as the pre-Chrsitian Greek ones, if not more. Broadly speaking, it can be classified into two categories :
Astika (Divine) and Nastika (non-divine).

Simply speaking, a person/school of thought is 'Astika' if they believe in any one of the three :
a) Divine authority of the Vedas
b) Soul
c) creator God

Nastika is the opposite.

The arrival of Islam saw the coinage of the term 'Hinduism', where every single Indic school were lumped into. If one notices the Islamic works on India, no effort has been made to even differentiate between Jains,Buddhists and Hindus !!

Only the Jains & Buddhists were organized enough to maintain their separation from Hinduism, if not to the Muslims, atleast to the Indian communities.

As a result, under Hinduism, we have every single thing available under the sun - old vedic polytheism, Vedantic monotheism as well as atheism.

Charvaka is the official, atheist branch of Hinduism.
Here is the reference:

https://en.wikipedia.org/wiki/Charvaka

As the reader will note, Charvaka is about rejection of all three 'Astika' principles and even rejection of Karma.

So my question is, why is a follower of Charvaka not acceptable to Atheist republic/why is Atheist republic denying Hindu Atheists ?

One would think, hindu atheists are natural allies, as we are the clearest, most obvious way to complete the turn of Hinduism into a cultural identity instead of a theological identity, yet, we are shunned.
Why ?