In many jurisdictions possession or distribution of certain information or content is illegal. Illegal primes, classified information, magnet links to copyrighted torrents, hate speech, outlawed pornography, incitements to terrorism, etc. Not all of this is efficiently encoded in the blockchain, but at least some can be.
Let's say a wealthy malicious actor wanted to disrupt the bitcoin network or crater the price. He could subsidize transactions containing illegal content. Moreover he could most likely do this anonymously or near-anonymously.
One or two instances would most likely be ignored by legal authorities. But persistent violations would most likely raise the ire of the courts. US federal judges regularly issue injunctions taking down websites. It's unlikely that they would make an exemption for block chains. Especially considering that most judges are technically illiterate.
Since all full nodes would contain the illegal information, it would become illegal to run the existing blockchain in the US. It would probably be impossible to enforce against your typical home user. But any public facing wallet provider or large-scale miner based in the US would be shuttered. GDAX, Coinbase, all the wallet providers, all the US-based exchanges, etc.
The scenario would be extremely disruptive, and either require a hard fork or make bitcoin untenable in the US. Very likely it would crater the price, as nearly all US demand leaves the market. Is there any possible remedy if such a situation were to occur?
EDIT Re duplicate question: The designated answer to the original question is fallacious. The assumption is that the protection of ISPs would extend to blockchains. Even if that was exactly true, it's still insufficient to protect against this attack.
Yes, US law exempts ISPs from copyright infringement liability. But only if they remove the offending content. A federal judge would likely extend the same logic to the blockchain in question. The only way to remove content from the chain is to hard fork at the point it was inserted.
Not only would that reverse all transactions that occurred subsequent to the offensive content. It would likely destroy split the currency every single time a content violation block is added. Theoretically that could be every single block. From the standpoint of US compliant parties, the network would be unusable.