According to this article from the Guardian
unknown persons are using bitcoin’s blockchain to store and link to child abuse imagery
“Since all blockchain data is downloaded and persistently stored by users, they are liable for any objectionable content added to the blockchain by others. Consequently, it would be illegal to participate in a blockchain-based systems as soon as it contains illegal content,” the researchers wrote.
This as well as other possibilities (the article also mentioned distribution of malware) shows that blockchains can be used to store illegal information, making downloading and possessing it potentially illegal. While it is quite possible that blockchain users wouldn't all automatically be arrested, it provides a simple case for arrest against individuals possessing such a blockchain if needed. Therefore, the use of this technology would become a legal gamble, because investors who are not programmers or can't afford to hire some (or lawyers) would face a certain risk of imprisonment, at least in some countries.
Does this mean that most or all current cryptocurrencies could become potentially illegal/useless?
This question is different from that one because I focus on the legal implications of end users. While a company that unintentionally hosts illegal material may be protected by ISP-like laws in the U.S., users of the blockchain provided by the company can basically come from any nation of the world, and in some the mere possession of illegal material in digital form by private people is forbidden (e.g. the Guardian article explicitly lists Germany, the U.K. and the U.S. as such nations). The accepted answer in the other article also seems to assume that illegal content could be detected before it is downloaded, which is simply not true. The assumption we have to make here is that by using the service the user unintentionally downloads illegal content.
The reason I ask this here instead of Law.SE is simply because I thought it would be more on-topic here, be of high interest for the community of this site and surely someone law-experienced is also found here. It would also be interesting to hear the opinion of people which may make more or less a living of this technology or are about to and the opinion of people who have a deeper understanding of the financial markets.