Don't let basic income advocates evade the question of who pays for their utopian scheme.

We absolutely shouldn't let them evade that question. So I'll go ahead and not evade it for you.

No matter how you arrange your basic income scheme (and the tax system to support it), it's going to split the population into two groups: those who are net recipients of government money, and those who are net contributors.

This is incorrect. Other commenters rightly point out that the benefits of basic income extend far beyond what can be measured in terms of money. But even if we only take into account the money, your assumption that you need taxes to support basic income is wrong. Money is not zero-sum. The money supply (including deposits, credit, etc.) expands and contracts depending on the needs of the economy.

Without making a rigorous argument, I will boldly assert that we can pay for a basic income without taxing anyone. We can pay for it through deficit spending or helicopter money (money-financed fiscal policy), which are both essentially the equivalent of printing money. You might worry that such a practice would cause inflation or devaluation of the dollar thereby resulting an implicit tax on those who have a lot of money. Here's two reasons why basic income through printing money wouldn't cause inflation:

1. Prices are determined by the amount of spending in the economy relative to the amount of real wealth* being traded. For some (inelastic) spending, people will spend whether they have the money or not. They'll borrow in order to spend. If you give them free money, they'll borrow less. The Fed can raise interest rates to make sure this happens. You're just swapping an unstable form of credit money for stable base money that never has to be paid back.

2. More spending isn't necessarily inflationary either. Most of what we produce is subject to an economy of scale. That means that the more of it we make, the cheaper it gets to make each individual unit. If you give poor people money to buy things they otherwise would not have bought, we make more of that stuff to meet the new demand, and prices can remain stable or even come down. Rich people benefit too because they have more customers to sell to. The money we hand to the poor doesn't just stay with the poor. It ends up in the hands of the rich as usual.

EDIT: 3. Money gradually leaves circulation over time. People hoard it and save it. If we're not continually injecting new money into the economy, we run into trouble. A basic income is as good of a way to do this as any. It's certainly better than incentivizing a bubble in private credit.

EDIT: 4. As technology advances, we produce more and more real wealth. If we want prices to remain stable, we need more and more money circulating. So we need to inject more new money than just what's necessary to replace the money that we lose through saving/hoarding.

A fun thought experiment is to ask yourself what would happen if the taxing arm of the treasury had no direct access to information about how much spending the government was doing and vice versa. Instead, they had to make decisions about how much to tax (and spend) based on macroeconomic indicators such as inflation. Would the budget naturally balance itself? Unlikely. We would run a deficit because that's what's most stable. We just wouldn't know we were running a deficit.

I would argue that for a government that can issue its own currency, we shouldn't think of taxation as a way to fund government spending. Instead we can think of it as an economic policy tool to remove excess money from the economy. But we have other tools to do that too (e.g. raising interest rates or fractional reserve requirements).

Paying for a basic income is cheaper than withholding a basic income. Instead of asking how we pay for a basic income, we should be asking how we expect to be able to pay for all the job creation/job protection we seem to think we need.

I know you probably disagree, but that's okay. I'm happy to discuss all of this further if you'd like to know more.

* - I'm defining the real wealth of a product or service to be the mean marginal utility across all people. For example, the real wealth of a luxury car isn't much higher than the real wealth of a normal car. This is because most people in the world would get a similar boost in marginal utility out of owning either one. A rich person will spend their money on less real wealth compared to a poor person because, for example, they'd get more personal utility from buying a luxury car than they would would by spending the same amount of money on two normal cars, even though the two normal cars represent nearly twice as much real wealth.