I need to power 20 5V RGB LED strips, each consuming 1A at full white. I'm working with off the shelf 10A supplies, so technically I can power them all by combining two 10A supplies.
Multiple independent supplies can be used if required, as long as they all share a common ground.
If the grounds are combined and LEDs are driven by drivers that are related to LEDs on the same supply it should not matter that your Arduino controller derives its supply from one or other 20V power supply.
If the LED supply is from V+ via LED to say MOSFET to ground, and Arduino supply is 5V, shares the same ground and drives the FET gate, then the source of the 5V and the source of the 20V is unimportant. The common ground is the essential factor.
Even if the switches (MOSFETS here) are on the "high side" between +20V and LED then as long as the control signal is translated up to the FET gate correctly the source of one or more 20V supplies and of the 5V supply may be independent as long as they share a common ground.
In this diagram, 20V supply A, 20V supply B and 5V supply C may be separate power supplies, with their ground (negative) connections joined.
Circuit A uses a "low side driver" and circuit B uses a "high side driver", both driven from the ground referenced controller on circuit C.
simulate this circuit – Schematic created using CircuitLab