Is an RJ45 / 8P8C connector a good way of connecting an Arduino to a simple device / circuit?
The cable would be about a metre in length
The current is about 40mA
The code is currently running about 50,000 times per second (I think), but it doesn't really need to if that's going to affect the cable choice; 1,000 times per second would be fine
The shift registers are both 74HC165

Based on that, it would be fine. RJ45 connectors, and Cat5/5e/6/6e cables have low resistance, and are designed for high frequency communication (Fast Ethernet and Gigabit, 100MHz and 1000Mhz respectfully). 100 METER runs without active repeaters are standard. And POE standards allow for up to 25 Watts of power over standard Cat 5e cable. That's 5 Amps at 5v.
You arn't even at 1% of the maximum rating for either RJ45 or Cat5.
An off the shelf ethernet cable and some RJ45 jacks would be your best bet. Don't even bother with crimping your own.