These categories would be better named as genetic/biological and environment/ideas. (I'll use mixed terminology, the important thing is to bear in mind what it means.)
Without genes, you won't get a person. Genes create the brain. If genes were different, you'd get a body without a brain or lungs, or nothing larger than an egg. And different genes, in the right situation, make a flower or a tree instead of a person.
Without environment, you'd never get a person either. You think eye color is purely genetic? Not if the fetus doesn't get enough nutrition from its environment. It will die without having eyes, without an appropriate environment to help it.
So, trivially, all traits have nature and nurture involved.
Now let's consider a liberal. Why is he a liberal? How can we explain it? It's a matter of ideas. There is nothing in his genes about liberalism.
Liberals are liberals because they have *knowledge* about liberalism. What is the origin of that knowledge? It's from our culture and its political traditions, from books, from thinking, from discussions, from the TV, and so on. Liberalism isn't a part of our genes, even though, yes, our genes are necessary for creating the brain which is needed to understand liberalism.
There's always an idea-based explanation of why a person is a liberal, which explains where the knowledge came from. His parents told him, or he figured it out himself, or he read it in _Liberalism_ by Ludwig von Mises, etc, he did not find liberal arguments in his genes.
Note that "knowledge" is not "justified, true belief". There is no assumption that knowledge isn't mistaken or that the holder understands its nature. Anti-liberals have knowledge too, even though liberals and anti-liberals can't both have the truth of the matter.
The nature/nurture debate -- the heart of it, I think -- revolves around questions like:
1) Where does the knowledge that determines if a person is liberal/happy/smart/gay/light-hearted/extroverted/many-other-things come from?
2) If a person wants to change, what interventions will be effective?
The "conventional/standard" view among *lay* people and the news media gives the following answers:
1) Around 20% of the knowledge for high level personality traits and other uniquely human features (things not found in animals) is from genes, and 80% from upbringing/etc.
2) If the knowledge is from upbringing, then it can be changed by learning new ideas, but if it's from genes then it's permanent/unchangeable.
BTW this view has sometimes been claimed to be a consensus of scientists, but it's not. For example, the expert geneticist Sahotra Sarkar not only disagrees but reports that most competent geneticists know that the heritability approach has been criticized in the literature and use other, better methods instead. The heritability approach these conclusions largely come from is popular with social scientists, psychologists, other people who haven't specialized in all the technical details.
My answers to the questions are:
1) All high-level, uniquely human traits (such as being extroverted, liberal, or good at thinking aka intelligent) are best explained by ideas, not genes. There's no gene about extroversion or how to enjoy critical discussion. The knowledge for those traits is in ideas.
2) Humans are not unchangeable, but interventions are sometimes hard b/c *ideas can be entrenched*. Interventions on all issues are possible, and often interventions are *easier for genetic traits* than any of the hard-to-change ideas. If something is really hard to change, that hints it's an idea, b/c ideas are often the hardest thing to change.
Often people argue against nurture by saying "it can't be nurture, b/c i tried to change that aspect of myself and failed". This is quite irrelevant to a correct framing of the issues. There has never been any serious argument that ideas are easy to change, or genetic traits hard; it was just assumed.
Things are hard to change based on how much knowledge there is to prevent change. Ideas can and do often have more knowledge than genes.
Entrenched ideas are hard to change for two big reasons: 1) there is more knowledge behind them to keep them entrenched (b/c memetic evolution goes much faster than genetic, so they are more highly adapted). 2) People use creativity to maintain and defend entrenched ideas (i.e. they create more knowledge). When you try to change a genetic trait, that's a static obstacle, but a memetic trait will sometimes change in the middle of your attempted intervention.
As I like to point out, hair color is genetic but it's not very hard to change it with hair dye. Height is genetic, but it's not very hard to wear platform shoes or stilts. Eye color is genetic, but it's not hard to purchase colored contacts. Having two legs is genetic, but it's not that hard to cut one off, if you want to change your leg quantity. But being a Christian, for example, is a matter of ideas, and for most Christians it's very hard to change.
Another idea people struggle to change is romantic love. Often enough people find their way of falling in love isn't working out very well for their life, but after several broken hearts they still have a very hard time changing it. Some people think this indicates it must be genetic, but that's a bad argument as above. And anyway we know historically that people treated love very differently in other cultures in the past, so how can it be genetic? There's simply a common, unscientific assumption that if people's attempts to change something fail then it must have a substantial genetic component.
I focus mostly on the issue of changing traits because I think that's what most people care about (and indeed it is important).
When it comes to changing traits, the most accurate single sentence would go something like: "It's 100% nurture, but that doesn't mean changing will be easy, you may want to study epistemology, i.e. to learn how to learn, or your attempts to learn new ideas may well be ineffective".
Another single sentence, "Humans are all about ideas, *ideas have consequences* (e.g. determine the course of one's life), and while changing one's mind can be very hard, it's always possible and doing it effectively is one of the most important skills to learn."
Another: "Blaming one's failure to change his mind on genes is a way of abdicating responsibility -- much like blaming a child's disobedience on a physical, genetic, 'mental' illness like ODD -- but in addition to playing the blame-and-victimhood game it's also a way to *give up* and stop trying to improve."
One more: "Nature does not have a 20% influence; percentage is the wrong thing to measure in; it's more of a constant amount, e.g. 20, which doesn't go up as our culture becomes more advanced, but instead becomes trivially small to overcome." (Example: to a low technology culture, changing eye color for a play would seem quite hard. But now it's easy. There was a fixed amount of difficulty which is now beneath us.)
This is not a comprehensive statement. Questions are welcome.