Are there any religions that believe in Karma (relating to reactions to self), but not reincarnation?
Is it really possible, considering that very obviously people do not always incur equal reactions to their actions in the same lifetime (murder, for example).
If you believe in karma, but not in reincarnation, how do you believe the system works?
I don't think any supernatural proposals of Karma can adequately work without reincarnation. As you have said, people do not always (or arguably, even usually) receive equal reactions of their actions.
I don't particularly believe in reincarnation, but I believe in karma in the general, imperfect, non-supernatural sense, where one can generally expect acting morally to provide them with moral returns, and where one can generally expect acting immorally to provide them with immoral returns. Acting malevolently or carelessly can lead to people not liking you or treating you well, and it can affect your conscience, and can lead to a life devoid of love, and in extreme cases it can cause people to take negative action towards you. Acting benevolently can lead to people respecting and liking you, helping you if you need it, loving you, and usually leads to a clean conscience. In addition, actions regarding the self usually come back to help or haunt you. Eating healthy and exercising, and abstaining from poor health choices will usually result in better health and beauty, while having negative habits will often lead to a reduction in health and beauty.
But due to luck or skill, some people who perform malevolent or careless actions will not reap negative consequences that equal their actions. And most nice people around the world in disadvantageous conditions will not receive anything to make up for their misfortune. Nature, in the form of either medical problems or natural disasters, affects the just and unjust alike.
I think supernatural proposals of Karma require reincarnation to be true to continue to be non-falsifiable.