Karma and reincarnation are an inevitable part of Indian culture, and Buddhism was also touched by them. Karma is understood as the effect of your intentions, rippling across causal chains, and through some of those causal chains, influencing your future circumstances.
I have to preface by not saying that I'm not a Buddhist myself but that I do my meditation in a non-Buddhist framework. That means I do have my fair share of experiences but I do have to translate between frameworks.
Of course karma is all about causal changes but a lot of the causal changes that Buddhists see don't really lend itself to materialist reductionism.
More importantly if you say karma is the effect of your intentions rippling through causal changes, that doesn't answer the question of why the whole "goal" of Buddhism is to move beyond karma and become enlightened. It doesn't even tell you what that "goal" is supposed to mean.
To me your answer looks like you are just reciting the teachers password. If I would go to an advanced Buddhist teacher I doubt that he would tell me that karma is about influencing your future circumstances because Buddhism is about being in the now, being in the moment.
Reincarnation is something I have more serious problems with. For one, I do not believe it. It is not a mandatory belief, though (nothing is, actually).
Of course Buddhism has no mandatory beliefs but if you drop reincarnation and keep karma you are left with asking where all that karma that determines your life comes from if not a previous life. In some sense it's a valid Buddhist position to not seek for a source but if you a a reductionist, then part of that means actually breaking things down and not just stopping at saying that the karma comes from somewhere.
Of course Buddhism has no mandatory beliefs but if you drop reincarnation and keep karma you are left with asking where all that karma that determines your life comes from if not a previous life.
From the actions of other people? One part of Buddhism is to de-emphasize the concept of 'self', so the difference between "good/bad actions will cause good/bad things to happen to future reincarnations of me" and "good/bad actions will cause good/bad things to happen to other people in the future" might be smaller than it would seem at first sight.
I'm afraid I haven't properly designed the Muggles Studies course I introduced at my local Harry Potter fan club. Last Sunday we finally had our second class (after wasted months of insistence and delays), and I introduced some very basic descriptions of common biases, while of course emphasizing the need to detect them in ourselves before trying to detect them in other people. At some point, which I didn't completely notice, the discussion changed from an explanation of the attribution bias into a series of multicultural examples in favor of moral relativity. I honestly don't know how that happened, but as more and more attendants voiced their comments, I started to fear someone would irreversibly damage the lessons I was trying to teach. They basically stopped short of calling the scientific method a cultural construct, at which point I'm sure I would have snapped. I don't know what to make of this. Some part of me tries to encourage me and make me put more effort into showing these people the need for more reductionism in their worldview, but another part of me just wants to give them up as hopeless postmodernists. What should I do?