Yes, it can be (depending on what you do).
Arbitrary doesn't just mean treating individuals differently (discrimination) without a proper legal justification. It also applies to any government or business that overextends their legal mandate, by subjecting people (even if equally) to limitations that have no legal basis.
I'm well aware that this rather quickly conflicts with some almost religious belief that anything can be limited through contracts, EULAs and TOSes (as long as its done voluntarily).
When people have alternatives, without such limitations, one can argue that people still have a freedom to do things differently. When a product or service becomes some kind of necessity, or not using it somehow becomes a personal limitation of its own, then such contractual limitation essentially have just created a new "law" outside of the only official process that is supposed to govern the creation of laws.
Businesses who create rules that essentially function like "private law", and governments who create laws without proper legal mandate/justification, are guilty of arbitrary behavior. Not because they treat individual people differently, but because their treatment all people is itself an arbitrary choice. As in, it lacks legal justification and goes beyond the legal authority that such a government or business has.