Which religion has not changed with time?

The Vedic religion, called sanatan-dharma, has not changed over time.

Sanatan-dharma, or the eternal religion, is called so, because it stays the same eternally. If a religion changes over time, say, to placate public opinion, or to jive with the particular times it appears in, it is not really religion, but politics.

According to sanatan-dharma, God has 3 main energies - the internal potency, which manifests the eternal, spiritual world; the external potency, which manifests the material world, and the intermediate or the marginal potency, which is the individual souls. The soul is called tatastha-shakti, or marginal, because it either can be under the influence of Krishna's internal, spiritual potency, or His external, material potency.

The soul possesses a minute degree of free will in that it can choose to be ruled by God's internal potency, or by His external potency. The soul is never independent like God, it is always governed.

When the soul is governed by by Krishna's spiritual potency, it exists in its original position of eternity, knowledge and bliss. When it is governed by God's material energy - Maya - the soul exists in forgetfulness about its real position, mistaking itself to be its material body and mind.

Bhakti-yoga, or devotion to God, is the scientific method of leading the soul back from its present deluded condition to its original position as part of Krishna's spiritual energy.

And that is also religion. The word re-legare, from Latin, means to re-connect. We know the word lego, which means 'I connect'. So religion is not just some sectarian belief in God, like less intelligent people like to assert, it is a process by which to connect to God.

The same word in Sanskrit is yoga, which means to connect or to unite. Again, we know that from the English word yoke, as in 'he yoked the ox to the wagon'. So yoga or religion is the science of uniting with God.

Naturally, such religion remains the same throughout all times. It’s like mathematics - mathematics don’t change over time, two plus two is four, always.

The best way to acquaint oneself with the eternal religion is to read Bhagavad Gita.

Krishna says:

My dear Arjuna, because you are never envious of Me, I shall impart to you this most confidential knowledge and realization, knowing which you shall be relieved of the miseries of material existence. (Bg. 9.1)

This knowledge is the king of education, the most secret of all secrets. It is the purest knowledge, and because it gives direct perception of the self by realization, it is the perfection of religion. It is everlasting, and it is joyfully performed. (Bg. 9.2)

Hare Krishna, Hare Krishna, Krishna Krishna, Hare Hare

Hare Rama, Hare Rama, Rama Rama, Hare Hare

"This mantra, consisting of 16 words and 32 syllables, is the only means against evil in the age of Kali. After searching through all the Vedic literature, one cannot find a method of religion more sublime for this age than the chanting of Hare Krishna."

--- Kali-santarana Upanishad