I believe that fundamental human morals do exist. A recent round-table discussion in my family centered on the question: Which came first, religion or morals? I started out all alone on the morals-first side and ended up converting everyone else - I doubt I’ll be so successful here.
Let us consider the wolf pack, for example. A pack often contains several fertile adult breeders, with all of the sexual instincts and drives intact. However, except in times of great plentitude, only the alpha male and female will mate and produce pups. The other pack members restrain their own sexual and reproductive instincts and instead cooperate in feeding, caring for, and training the pups of the alpha pair. Wolves have evolved so that this behavior is necessary to their survival - they function best in a social group, and certain rules are necessary in order to maintain that social group.
Aren’t these rules of behavior identical, in theory, to what you refer to as human morals?
Like wolves (and various other pack and herd animals), humans are a social species - they require some sort of social group in order to survive and reproduce successfully. Any social group must have rules of some sort in order to exist - otherwise the group falls apart and the individuals fail to thrive and reproduce. So fundamental human morals do exist - you are simply being too ‘modern’ in your thinking.
Although I’ve not given this any deep thought, a quickie guess at some fundamental human taboos would be (in no particular order) 1) murder (as opposed to killing - I’ll explain that if needed); 2) theft; 3) rape of someone else’s bonded mate; and 4) infanticide and/or euthanasia of the elderly, handicapped, etc. in times of ease and plenty. And bear in mind that these actions would only be taboo within that social group; the same actions performed against members of a rival social group would most likely not only be ‘legal’, they may even be encouraged, at least until some humans entertained the concepts of cooperation, treaties, trade, etc.
Incest was probably discouraged but not strictly forbidden, as an isolated tribe stricken by a fatal disease may have no other option for survival.
I think a cannibalism taboo would be dependent on what type of cannibalism you mean - ritualistic cannibalism involving the eating of selected body parts (such as the heart) of deceased, highly-respected tribe members or warriors/hunters of rival groups might have been quite common. However, cannibalism as a common food source would most likely be another case of ‘only in dire necessity’. It’s otherwise a little contrary to survival, don’t you think?
Genocide? Rival tribes probably fought frequently over prime ‘ease of survival’ territory, and ‘genocide’ undoubtedly occurred fairly often, as far as vanquishing a rival tribe was concerned. However, true genocide was probably rare; all of the males in a defeated tribe, from infant through elderly, would most likely be killed, but the females would be spared and incorporated into victorious tribe as slave labor and/or mates. Female infants may have been spared both as future mates and to both pacify and inhibit their mothers. But while the defeated tribe may have ceased to exist as a separate entity, its genes and some of its knowledge and tradition survived through the preserved female line.
And pedophilia - I’d say that probably depends on your definition of pedophilia. Sexual play with youngsters, even infants, that involved fondling and such may have been considered simple innocent fun, but sexual activity that could cause the injury or death of a very young child would almost certainly be forbidden. I doubt that pure pedophilia (primary sexual attraction to infants or obviously sexually immature children) was seen very often in early human development. Despite recent claims that pedophilia is simply a ‘sexual orientation’ like homosexuality, it is undoubtedly a serious personality disorder - pedophiles prefer children because they (pedophiles) are emotionally unable to form a satisfactory adult relationship. They can only feel safe in a relationship with someone so much smaller, weaker, and emotionally vulnerable than themselves that the victim presents no physical or emotional threat to the pedophile. Some pedophiles are also basically power-assertive rapists who enjoy the sexual domination of another human being but are too personally inadequate (cowardly) to assault an adult. The point of all of this rambling is that 1) the cultural and societal pressures that create pedophiles were probably pretty much non-existant throughout most of early human development; and 2) those with pedophilic tendencies would display other, more obvious and debilitating character traits that would most likely result, in one way or another, in their elimination from the social group at a fairly early stage.
Basically, what I’m trying to say is that a taboo would not exist before the concept and possibility of the action/behavior existed. For ‘fundamental, universal morals’ you need to go way back to very early human development and try to determine the most basic, elemental rules required for a group of humans to live together in a cooperative, mutually beneficial society.
This is just IMO, of course, although I can most likely dig up some references to support some of this. The rest of it is just pure speculation. 
JET, I’m going to have to call you on this one and ask for a cite. I don’t want to add a great deal to an already lengthy post, so I’ll just toss out a couple or three brief comments.
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Cannibalism, by definition, is restricted to meat-eating animals - I don’t think I’ve ever heard of a single instance of a horse, cow, or sheep knowingly and deliberately eating another member of its species, or even one of another species! Herbivores are rather plentiful, while carnivores and omnivores are comparatively rare, so the ‘common’ occurence of cannibalism in the ‘animal kingdom’ is actually going to be restricted to a rather small, specific group. Cannibalism may be more common in the ‘animal kingdom’ than among humans, but that’s a different statement entirely, isn’t it?
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Incest is extremely common in the ‘animal kingdom’! Do you have any idea at all of how, for example, herds of horses conduct their lives in a natural state? Have you ever so much as glanced at any information about animal breeding and encountered the term ‘inbreeding’? Honestly, I don’t mean to be rude, but this human misconception is so common and so laughable to anyone with much knowledge of animals that it is actually the butt of a rather old and stale veterinary joke!
You might want to reconsider that statement.