In Anno 1800 Royal Taxes are never really explained in any great detail, but it is important to understand how they work if you want your city to run as efficiently as possible.
What Are Royal Taxes
Royal Taxes are levied against your city when you hit a certain number of residents in a specific tier. Once you hit 1000 citizens in a Tier, that Tier will be subject to Royal Taxes. The percentage of the money you need to pay in the form of the Royal Tax seems to be affected by how many citizens over 1000 you have in that particular Tier. It is also important to note that Royal Taxes are Tier specific, so if you have over 1000 Farmers, and under 1000 Workers and Artisans, you will only be paying Royal Taxes on the Farmers.
From a gameplay point of view, Royal Taxes are designed to force players to move outwards to different islands, instead of just trying to crowd their entire Empire onto the starting island. As such, the only real way to keep them low is to ensure that you do exactly this. Make sure you are settling new islands and setting up Charter Routes to ferry the goods you need between them. Paying for some Charter Routes is much cheaper than paying Royal Taxes. If you don’t do this, the only real way to reduce Royal Taxes is to reduce the number of residents, and this will leave you with a worker shortage unless you also shut down some of your business, factories, and farms.
Over on the Anno 1800 Reddit, the developers have admitted that the way Royal Taxes work and are calculated, could be a bit more transparent, as such, we will be sure to update this guide when they make more details about how they work public.