From a family relationship pov, how far from the throne does a royal have to be before he or she has to work for an income instead of being tax subsidised?
The Queen has her own properties and income, so in theory she could live on that without needing to “work for a living” or be “tax subsidised”.
As for other royals, according to Wikipedia:
That’s up to the Queen.
The only people who receive a direct subvention from the taxpayers are (a) the Queen, who gets a “sovereign grant” (36.1 million pounds sterling in 2013/14) and the Duke of Edinburgh, who gets a parliamentary annuity of 359,000 pounds.
In addition to the sovereign grant, the monarch is supported by the income from the Duchy of Lancaster (a portfolio of land, property and assets) and by the revenues of her personal estate, but these are comparatively modest compared to the sovereign grant.
The Prince of Wales has his own revenues from the Duchy of Cornwall, another (larger) portfolio of land and assets). These support not only him and his wife but also the Cambridges and Prince Harry.
Other members of the royal family get (or don’t get) money out of this pot if the Queen decides to give it to them. In general, it goes to royals who carry out engagements or discharge functions on behalf of the Queen. But direct cash payments aren’t the only way that lesser royals can be supported; they can, for instance, be given residential accommodation for free, or at below market rates.
In addition, the money supplied to the Queen and the Duke of Edinburgh aren’t for their personal use, but are to meet costs accrued by their responsibilities. To consider it anything like a salary (I know it’s not a word OP used) would be akin to including the costs of running the Presidency to Obama’s salary.
Technically, only the Queen and Prince Phillip get money from taxpayers. It’s called the civil list, though it’s not really a list any more.
The others get their money either from the Queen, in which case it’s either a gift or money earned for performing duties (or at least it’s supposed to be the latter) or from their landholdings; those are supposed to be taxable but Charles, at least, uses some dodges like charity status to legally avoid some tax. Anyone can get money from landholdings if they own the land, so it’s not exactly the same as getting money from taxpayers for being a royal. They don’t need to work for a living but then neither do many landowners.
Several of the Queen’s family members do have paying jobs anyway. Andrew was a fairly senior military figure until he retired (and he really did fight in the Falklands War), Harry is still in the army, Wills was a helicopter pilot, Anne’s children both have fairly normal jobs, and Edward runs a media company. So you only have to go to her own children before you find people in normal paying jobs, although the income from them will be dwarfed by whatever they get from trusts, lands etc, and all the adult titled ones - titles other than Prince or Princess - have some landholdings.