Neo-edelexianism is the ideology of edelex after accepting the non-aggression principle. It's 
socially progressive, civically 
libertarian and economically 
capitalist. Ethically, it is a minimal moral realist and deontologist. It is from this framework that most of its politics are derived.
Government
Neo-Edelexianism is civically libertarian. It supports the total legalisation of all actions that do not break the non-aggression principle. This includes all consensual sex acts, all taking and selling of drugs, and assisted suicide. All immigration and 
'copyright violation' should be allowed unconditionally. It is mostly anti-democracy, believing that tyranny of the majority is a legitimate concern and the rights of individuals should not be violated by the state in the name of 
popular opinion or the 
'greater good'. It also believes that democracy does not always bring society the best results, as can be seen with brexit. Thus, its influence should be limited to small initiatives by local governments for projects such as building local parks. It should be noted that people are free to practice democracy within their own private property.
Philosophical and Psychological Foundations
Edelism is generally psychologically 
egoist, rejecting humanism. It believes that groups form from common self-interest. It therefore believes that wide-scale society and technology are generally bad descriptively 
, although thinks their development is inevitable and its slowing is a waste of time.
Most of its philosophy lies in its metaethics, being a minimal moral realist. This means that it accepts that moral claims express truth-evaluable propositions, that some of them are true, but not that there are real moral properties.
To justify the first part, also known as the semantic thesis, it uses the Frege-Geach problem. This is a critique of noncognitivism (the idea that moral claims just express emotions and so cannot be true or false) which states that the ability to embed moral claims into more complex sentences leads to an inconsistency in what the moral claims express if noncognitivism is true.
The second part, the alethic thesis, is justified with its justification of the 
non-aggression principle, which is the following: There is an objective truth, and therefore some conclusions are objectively more rational than others. If some conclusions are more rational than others, then the act of concluding some things is more rational than the act of concluding others. If actions can be somehow based in truth and therefore rational, there must be normativity, or 'ought' claims involved. Therefore there are ought claims about reasoning. If you are then obligated to act with your body in some way by reaching conclusions, you must have rights over your body, and a right to exclude others from it so you can freely fulfill your obligations. Someone else violating this right would therefore be immoral. Now we have self-ownership, if we want to own other things, we must have a moral system which, if everyone were to follow it and have full rights to defend their property, there would be no violations of another's self-ownership. This system is the NAP.
It should be noted that as animals cannot be held to epistemic norms ('ought' claims about reasoning), they are not held to the NAP under Neo-Edelexianism.
It is metaphysically materialist, antirealist about causal relations, and atheist (due to lack of reason to believe in God).
Economics
Economically, Neo-Edelexianism roughly aligns with 
Friedrich Hayek. It supports an almost entirely free market, 100% private business freedom as a natural consequence of the NAP, with the state only stepping in when absolutely necessary to ensure people's wellbeing, preferring mutual aid and charity where possible, due to the knowledge problem. It generally believes that we should try to avoid reliance on the state, and we should develop more mutual aid and charity. It is also 
Georgist, only supporting taxes on (effectively collectivising) scarce, unproducable resources (land/natural resources), and pollution, as the former was appropriated from the commons and the latter is damaging the property of others. It generally tries to avoid nationalisation but for military, police, courts and some land, it may be necessary. Microeconomically, it accepts the 
subjective theory of value, and macroeconomically is sympathetic to the 
monetary theory of value.
Foreign Policy
Edelism supports a 
hawkish foreign policy, supporting the 1999 NATO intervention in Yugoslavia, the 2011 intervention in Libya, the war on terror in Somalia, and more skeptically, the wars in Iraq and Afghanistan, at least conceptually. Targeting governments exclusively is acceptable, however, side-effects of civilian property damage must be avoided and compensated for. It believes in increasing international accountability and enforcement of UN Security Council Resolutions through force, including against Israel's current crimes against the Palestinian people. When it comes to Israel, it believes that the West Bank and Gaza Strip should be Palestinian territory, and Jerusalem should be international territory, with semi-autonomous regions for Israel and Palestine, to mitigate apartheid and terrorism respectively. Smaller Israeli settlements in the West Bank should be destroyed and there should be land swaps to account for the bigger ones. Safe passage should be ensured between Gaza and the West Bank.
Social issues
Neo-Edelexianism is socially progressive, believing in the performativity theory of gender, being pro-gay marriage, and the idea that race is a social construct. It primarily differs from extreme social progressivism, however, in its skepticism around deplatforming, 'otherkin', xenogenders, and neopronouns. It believes discourse is essential and deplatforming is generally counterproductive, although it respects the right of private companies to have their own content policy. It believes that private businesses have the right to exclude others from their rightful property for any reason 
, and this includes on the basis of their sexuality, race, religion, or any other characteristic, regardless of Neo-Edelexianism's personal socially progressive views. It is 100% pro-choice up until the beginning of labour, and completely against gun control.