Well, first off, Buddhism teaches the concept of reincarnation (which is at direct odds with the Christian belief).
It does not exactly teach reincarnation. It teaches "rebirth". And that rebirth aka change is happening at every single moment in our lives. We are constantly changing, and what we are now today is not the same person we were a year or ten years ago. After death, our essential elements which make up our bodies will be recycled into the earth to nurture a new cycle of life. I don't find this incompatible with Christianity.
They teach that reincarnation occurs due to ignorance and suffering- and that one can stop it by becoming a Buddhist.
Not exactly. Rebirth (or change) is seen as resulting from craving for change, which leads to ignorance and suffering. Ignorance is dispelled by wisdom, and suffering is dispelled through understanding causality. This is not incompatible with Christianity either.
Different schools of thought claim different things. Theraveda Buddhism (the oldest form) doesn't believe there is forgiveness of sins (or negative karma), while Vajarana Buddhism believes mantras can help with this.
It is true that different schools/denominations of Buddhism interpret things different. I believe Theravada is the oldest and most authentic, whereas all of the (much) later developments (e.g. Mahayana, Vajarana, etc.) are transmitting corrupted versions of Buddha's original teachings.
Christianity believes we have eternal souls- Buddhism doesn't.
This is largely true. But, to be more precise, Buddhism teaches that there is nothing we can identify as our "eternal soul". It is not our thoughts, nor our feelings, nor our body, nor sensations we feel through our senses, as all these things changes.
The eight-fold path itself isn't really at odds with Christianity (especially everything regarding ethical conduct)- excepting the eighth one regarding meditation.
How is meditation at odds with Christianity? Meditation is taught in the Bible.
However- just accepting the eight-fold path doesn't make one Buddhist. You have to accept all of the Buddhist teachings, be part of a Buddhist community, and accept the Buddha.
Not so. The Anguttara Nikaya shows Buddha teaching that all things must be tested and verified by each individual, and to not rely on untested faith in him, the sangha, or the dhamma alone.
They generally consider a Buddha to be an enlightened/awakened/purified person who will help others to achieve the same state. Mahayana Buddhists look at the Buddha as a god-like figure. In fact- Buddhists believe in various spirits and demons- though they don't see them as gods (but the way they relate to them amounts to worship/appeasement/whatever you want to call it). However- Buddhists generally claim to be atheistic (as they believe ultimately everything will come to nothing and cease to exist- and that there is no ultimate creator) even though they directly relate to spirits and demons.
This is generally true, but I do not find these current-day beliefs to be in complete harmony with what Buddha himself taught in the Nikayas.
In fact- demon possession is not unknown in Buddhism. They have various oracles, who are people (monks, nuns, priests) possessed by specific demons which have been known to them for centuries. It even makes the Dalai Lama uncomfortable. This is a big red flag. The Dalai Lama has changed his views on non-Buddhists over the years. He's gone from believing that everyone should be Buddhist to recanting that belief. Now, he's even gone so far as to claim that Christ was a Buddha who reached enlightenment. While that's a nice thought- Christianity and Buddhism are two belief systems that are inherently at odds.
I don't consider Tibetian Buddhism (of which the Dalai Lama represents) authentic to the original teachings of the Buddha. It is a much later development, a thousand years after the Buddha died.
To me- despite the talk of enlightenment, etcetera- it seems like a hopeless belief system. Why bother at all if no matter what they teach you'll simply cease to exist one day?
Enlightenment is merely realization that everything changes, and is not who we essentially are. Ignorance and suffering comes from the false idea that things always stay the same, or to clinging to the idea that our thoughts, feelings, etc. are who "we" are. Releasing these thoughts, etc. brings relief.
