Parallel connection to Wiegand 26bit RFID readers
It looks to me like the Wiegand interface is an open-collector interface (like I2C), which is why they can be wired in parallel like that.

As long as the Arduino has both connections set to INPUT (not INPUT_PULLUP and certainly NOT OUTPUT) it shouldn't interfere at all.

By the way, for Wiegand, the two signals are DATA0 and DATA1.  To transmit a 0 the DATA0 line is pulled low. To transmit a 1 the DATA1 line is pulled low.

You should also check that the idle voltage on the lines is indeed 5V as it should be.  Anything more than that could cause the Arduino to chip the voltage to 5V through its internal ESD protection diodes.

Also you must ensure that the Arduino has its ground pin connected to the ground connection of the Wiegand system (which it should be since you are powering it from that).