It is surprisingly difficult to censor payments on bitcoin, for example. It is quite resilient to censorship. You might have to use special tools - you might have to use proxies, Tor, gateway servers. But if you are motivated enough, you can always make a payment. If you have bitcoins and you want to pay someone, it is really difficult for a government to stop a motivated person from doing that.
Think of it this way: when I make a payment using a credit card, via MasterCard, there are assumptions that I am making. My assumption is that MasterCard is trusted; that no one has hacked it; that there is no intermediate party that can somehow steal my data, make payments on my behalf, and then stop the notifications from coming to me. So there are assumptions you make about your adversary in these situations.
The assumption that bitcoin makes is that there is no adversary that has enough power to take the majority stake within the system. To me, this seems like a fair assumption, and a much more believable one than the assumption that MasterCard is honest, that MasterCard has not been hacked, and that there’s no one in between. Because I know nothing about MasterCard or the links that connect us, and the only way for me to check if there has been some sort of breach or someone has been misusing my card, is for me to go and check it with MasterCard - again, this entity I don’t know anything about. But with bitcoin, everyone can see what is happening. If I give you 5 pounds, it’s on the blockchain, and everyone can verify that Mansoor gave you 5 pounds. You cannot deny it later on, and I cannot use the same 5 pounds to pay someone else, because it’s on the blockchain, and the other person can see that I’ve already used it.
If there is a breach, it’s much easier to detect when it’s on a blockchain. Moreover, if a cryptocurrency is designed well, if you’re relying on proof of work or on some sort of proof of stake system, then it is much more difficult to breach than a traditional banking system.
If I am in China and I am behind the great firewall, it prevents me from going to websites the Chinese government does not like, so I can’t go to BBC.co.uk from China. The same great firewall can be used to block me from communicating with the rest of the bitcoin network, but there are ways for you to get past the great firewall. You use a VPN or Tor, and then you relay your payments through that system to bypass the great firewall. Although, if your adversary is someone who is physically going to come and shoot you, or put you in jail, then censorship in the real world is possible, of course.