Stephen Batchelor, a former monk in both the Tibetan and Zen traditions, wrote Buddhism Without Beliefs, an explicit attempt to separate the baby from the cultural bathwater in Buddhism. It's been ages since I read it, but if memory serves I believe Batchelor argues that Buddhism is a matter of practice and inquiry, not belief.

The history of Buddhist art tells you a lot about cultural accretion. Found this from the Met. "In the earliest Buddhist art of India, the Buddha was not represented in human form. His presence was indicated instead by a sign, such as a pair of footprints, an empty seat, or an empty space beneath a parasol." Compare that to florid Tibetan iconography.

What's great about Buddhism is that it adapts so well to cultures it merges with, from spiritually athletic Zen to belief-based pure land to compassion-based Mahayana to insanely ritualistic Vajrayana. There are all these "skillful means" based on the varying needs of sentient beings. Why would you want to limit yourself to what the historical Buddha and his contemporaries did or believed?

Edit: You might be interested in the way Tibetan Buddhists conceptualize the various vehicles or "yanas" of Buddhism, from renunciation - the original vehicle - to great compassion to radical acceptance. There are scholarly explanations, but Dzongsar Khyentse Rinpoche wrote an excellent one that compares them to ways of being in a cinema. Here

Hi there! This is a little outside my area of expertise and I'm sure some people will come in and much of this information was unfortunately taught to me by some professors at college in Bhutan, but I'll try to provide some sources where I can. And if someone has more sources for information I can't fully verify or can elaborate or correct me, please do.

First off, you're right to be overly specific in calling the Buddha (Siddhartha Gautama) "a follower of the ancient Vedic religion" as opposed to saying, "The Buddha was a Hindu." Hinduism is a modern construct associating the native Indian religious complex with a sort of national identity (a reaction against Islam being associated with Pakistani national identity). The religion, I was told by a Bengali sociologist, is properly called "Brahmanism" because as Christianity derives its authority from the Bible, and Islam from the Qur'an, the followers of native Indian religions used to derive their authority from Brahmins, or the priestly Varna (caste).

All Dharmic religions (Buddhism, Jainism, and Brahmanism) have the concept of enlightenment in the spiritual sense. So enlightenment isn't a new thing that Buddhism came up with, what IS different is that the Buddha taught that enlightenment was not contingent upon Varna. Before that, except for a few ascetics in the woods, it was commonly believed that only Brahmins could be enlightened, and that the other Varnas (Kshatriya, Vaishya, and Shudra) and outcastes would never be enlightened. Slaves (Shudra) would have to be reborn as a Brahmin if they ever wanted to get enlightened.

Contrary to popular opinion, the Buddha did not do away with Varna. He was human and a product of his times. While caste isn't SUPPOSED to matter in the Sangha, the Sangha still tended to run in an aristocratic fashion with monks possessing distinguished ancestry being at the top, while monks without at the bottom (with exceptions, of course).

A good place to start with the history of Buddhism is Andrew Skilton's "A Concise History of Buddhism." It's mostly a history of the texts with their context in mind but it does go over India before the Buddha.

Your question's a little vague though. It's kind of like asking how did the world of Jesus influence Christianity? Well, a lot of ways, of course. If you're a little more specific, I can start pointing you in more precise directions.