I've worked with Bitcoins, and I want to give a technical point here before answering.
Bitcoins is a virtual currency, completely different for what we have known as currency until now. It's not an archive, or similar. Then, how does it work?
It starts when anyone that's already in the bitcoins red, gives you bitcoins (or a part of a bitcoin) in exchange for real money, products or services. When they gives you "bitcoins" they are actually changing the ownership of that amount to your personal wallet, which is not necessarily linked to a name and personal information. In fact you can have several wallets (actually you SHOULD have several wallets if working with bitcoins) also bitcoins can be mined, through computational problems. This works due to a decentralized mining method, which means several computers around the world trying to solve a computational problem, in order to sign transferences. When a money transference is digitally signed by the winner computer, this computer is rewarded with a part of bitcoin. Usually this is not solved by a single computer, but by computer pools working all at the same time in one problem. This way you can generate new bitcoins at the same time the transfers are being signed in order to avoid its replication.
Then, why does it have such a bad fame? As mentioned, Bitcoins are not linked to any name or personal information, means it respect the anonymity of the user. This leads in many criminals using bitcoins to buy weapons, drugs and prohibited services. But the money itself is harmless, it's this use which generates such consternation.
I think yours is such an interesting question, as it actually refers to the right of completely anonymity on the internet. You were referring to ethical issues, but is it actually ethical to obligate anyone give his/her personal information? I think the use of the anonymity in general, is ethical, because it's just a tool. The misuse of the tool itself could be ethically doubtful, but buying a coffee should not be unethical, as you would be supporting a tool -legal tool-, or simply a digital easy-to-use currency, but not necessarily supporting crime. By your statement, also buying computers is ethically doubtful as it's used by criminals as well, or the internet itself. It's just the concept of anonymity what is a blurry line we are not used to treat with in our lives.
So I think before asking yourself if bitcoins are ethical, you should ask yourself about the ethics of internet anonimity.
I think you could enjoy reading about Snowden, Assange, and take a look at the EFF, TAILS and TOR projects to learn more about internet anonymity.
I hope this was useful :)