Of course, you never know who uses a multimeter for which purpose, so if there's the chance of people using the multimeter for things it was not designed for, you should get one with at least basic safety features, no questions asked.
However, for a device like the Arduino, which is quite safe already, cheap meters can be used. It might be best to replace the test leads with small clips or hooks so there will even be less mistaking that this will be a low-voltage, low-power measurment device.
I don't think the cheap multimeters are great, because they aren't, but specifically for the Arduino, there is no "too cheap," except if the multimeter will fall to pieces as soon as it's taken out of its packaging. I think they're quite painful to use due to their puny display, but even the cheapest multimeters are suitable to use for the Arduino. If my multimeter mysteriously broke down today and everything I could get was a cheap garbage meter, and I urgently needed to measure stuff on the Arduino, I wouldn't hesitate buying one. They're just barely suitable for extremely ballpark (too cold to touch, might be safe to touch, too hot to touch) temperature measurements (most of them come with a half-assed thermocouple), so they still are of some use as soon as your decent meter is working again.
I do think intrinsically safe equipment is quite worthwile, even the light fixtures in a bathroom. If the Arduino didn't have the relatively low current limitation, I also wouldn't recommend a cheap multimeter for it, because it can get quite nasty when measuring "voltage" with the leads plugged into the current terminals for even medium currents and crappy meters. With the Arduino's intrinsically safe current limit, this will probably just damage or destroy the meter (which is one of the reasons why it's a bad idea to buy an ultra-cheap meter), but that's about it.