max current while using a shift register
0.20A is not the maximum current for an Arduino device.  0.20A is the maximum current for the chip that is on the Arduino.  Thus it is only relevant to devices that are directly connected to the Arduino's IO pins (that connect direct to the chip).

The shift registers take their own power from the +5V pin, which is limited to between 500mA and 800mA depending on how you power your board.  Each shift register has its own power limits that are completely separate to the Arduino's main chip's power limits.