The essential problem I have with classifying the Carvaka as Hindus is that it is 1) historical revisionism of a sort, since the Carvaka considered themselves a reaction to Brahmanism and Vedic religion, both politically and epistemelogically and 2) it completely any and all philosophical presuppositions that even the Buddhists and the Jains have, namely karma, reincarnation (or rebirth if you are a Mahayana Buddhist) and so forth. Its materialist metaphysics negates the possibility of 1) God, 2) Liberation since there is nothing to be liberated from, and 3) Vedic authority, since they are lack any divine content. Moreover, they reject any and all notions of "dharma", misused word that it is, and assume an explicitly anti-Dharmic stance that associates itself with the satisfaction of desire to maximise happiness, which is hedonism proper. Like, Epicurean, Benthamite hedonism.
So, we don't even have the dharmic content that a lot of Neo-Vedantins (and dare I say Hindutvadis) use to turn Buddhism and Jainism into dharmic religions. We only have some cultural origin in reaction to proto-Hinduism, subjected to attack and in turn subjecting to attack astika schools of Indian philosophy (nebulous term indeed). It lacks any coherent connection or commonality except the fact that it accepts perception as a valid pramana. But then again, if we use pramanas as a means to ascertain what's Hinduism, we are having a major problem with considering the Madhyamika Buddhists like Nagarjuna who reject the existence of epistemology altogether as Hindus. So yeah, there is really no coherent way we can consider the Carvaka Hindus. However, the Samkhya were an atheistic Hindu school of thought, and a lot of the Mimamsikas were as well. Rather than glorify the dead school of the Carvakas, I would think we need to reassess these two schools.