In economics, there is a concept of "tax distortion". If you tax apples, then people change their behaviour: apples are essentially more expensive, so people eat fewer apples and eat more pears instead, and people have less money due to paying the extra tax, so they reduce their consumption of everything. A non-distortionary tax is one which has an income effect (that is, people becoming poorer and so reducing consumption) but no substitution effect (so there is no change in the relative prices of any goods).
There are three types of non-distortionary taxes. The first is the taxation of goods with an absolutely fixed supply, such as land. The tax does not affect demand, and cannot affect supply, so the price has to stay the same. A second non-distortionary tax is the poll tax, the tax on being alive. Finally, a consumption tax can raise the price of all goods equally, so that there is no change in the relative prices of goods.
I'm not aware of anyone previously having connected up these notions. It's worth noting that they are not the same: in my view liberal neutralism is also consistent with Pigovian taxes - that is, taxes on what economists call "negative externalities" - things like pollution, where one person unintentionally harms another in a way that is hard to enforce a legal right against.
For a state to fulfil liberal neutralism, then, requires it to abolish income taxation, inheritance taxation, sin taxes on sugar and alcohol, and move towards a consumption-tax system. This would of course be controversial, but I maintain that all objections which do not end up rejecting liberal neutralism are ultimately based upon misunderstandings.
Objection One: Consumption taxes are regressive
That depends upon what kind of equality you care about. It's true that philosophers tend to talk about wealth and income, but that's because they haven't really thought about what it means to have money which you don't spend.
Moreover, surely it's not important that the tax system be progressive so much as that the social system as a whole be progressive? If someone proposed a law to make "Jerusalem" the national anthem, you wouldn't object that the law failed to promote equality. Similarly, it's fine to have a possibly-regressive tax system if you combine it with a basic income; the combined effect will be similar to a negative income tax, and so will overall be progressive.
Objection Two: Okay, but there should at least be exemptions for staple foods and other essentials
Think about it this way: if everyone had plenty to live on, and there was no poverty, would it be a problem that tax was charge on these essentials? Surely it would no more of a problem than taxation of any other goods. This points us to the real problem here: that some people are in poverty and don't have enough to live on. But we can solve that problem by giving them money, such as through the basic income I suggested above. Compared to uniform taxation and giving poor people money, the effect of removing consumption taxes is to give a tax break to the well-off. If you're not convinced, read Joseph Heath (or listen to his interview on Rationally Speaking, which covers this ground).
Objection Three: This removes democratic choice
This is partly a question of how valuable you take democracy to be as an end in itself. If you believe that immoral things can be made moral by a democratic vote, then sure. Communities can have the right to levy whatever destructive and illiberal taxes they like. But if you think that democratic choice is constrained by justice, then liberal neutrality does indeed restrict the right of polities to tax in whatever way they choose.
Note, however, that we're still leaving room for a fair amount of democratic choice. Countries can still choose to nationalise industries. If you believe that state provision of education and healthcare free at the point of usage is consistent with liberal neutralism, which I think is highly plausible, then you can have that. And once you've decided exactly what services and benefits you want the state to provide, what exactly is left to decide? The actual rate of tax is just the government's budget divided by the total GDP, so it's not like there's a great deal of choice going on under any system (unless that choice is "let's have lets of spending now, put it onto the national debt, and our grandchildren can pay for it.")