I wasn't even speaking about bitcoin. I was speaking about traditional toxic waste and your yard.   Uranium hexafluoride in alumnium cans, if we must name something specific... My point being that your argument was generic, "Using Nicolas Dorier's lawn for other purposes is not abuse if you are willing to pay the price".  

In any case, going back to Bitcoin, no one is obligated to relay or mine any particular transaction; and might not do so if they think they're harmful by whatever criteria they're using. One need not define anything.

But to your question of "arbitrary", do you intend to insult me?   I do not think it is arbitrary to say that Bitcoin, which was created, operated, maintained, and adopted with the express stated purpose of being an P2Pecash system ... has an intended purpose of being a P2P ecash system, and that use of that that is using the system outside of its stated purpose. By comparison there are alternative networks based on the Bitcoin code base which have stated purposes which explicitly include other things; and, as a point of history, when someone first proposed storing name registrations in the Bitcoin system the system's creator vigorously opposed this and recommended doing so in an alternative network.

Uses which are not related to Bitcoin ecash and instead just ride atop it as a communication/storage channel (or worse, try to explicitly compete with the Bitcoin currency and replace it in the market while using Bitcoin's own network) are a pretty good start.   Case in point, we're in a thread where someone was upset because nodes were blocking transactions of theirs which were creating purposefully unspendable txouts (e.g. adding non-Bitcoin bloat to the UTXO set) in order to run a commercial service called "crypto graffiti" which does what it says on the tin. I think that this is indisputable abusive: It benefits nothing but it's operator/users to the cost of every current and future user of Bitcoin, it uses the system not as an ecash system (which is what virtually all of its users signed up for), but as a messaging and free perpetual data storage layer,  this (data storage) usage potentially risks subjecting node operators to nuisances (e.g. DMCA notices), and even the name acknowledges its nature. ... but on the scale of abusive things it's not very interesting: something can be abusive without being worth worrying about, as the overall behavior of the system already confines the amount of damage to uninteresting levels.  It's only worth mentioning that it's abusive by way of explanation as to why I do not expect this kind of use to be reliable.