SpinDizzy will be moving to 100% SSL connections sometime in 2019. This means clients which do not support SSL will either need to be upgraded or a new client used. The web client always uses SSL.
For Windows, the best option is BeipMU. This client is updated very frequently and the developers are extremely responsive. If you have windows 10, it is also available in the Windows Store for free. If you feel you are unable to switch to this wonderful client for whatever reason, you can use the Websocket gateway program Morticon wrote. Information is available in +read. Even if you switch to BeipMU, you may still find the gateway program useful because it can handle bad/flaky connections.
For Linux, the best option is running BeipMU in WINE, or to download and manually compile the latest TinyFugue. It may also exist in package format for your distribution. Trebuchet Tk also supports SSL if you install the tcltls package.
MacOS users can try Atlantis, though it does not appear to be updated or supported any longer.
Phone users currently have no known clients which directly support SSL. They can either use the web client or a proxy/tunneling program that will tunnel the connection. Android users can also try installing TinTin++ under Termux. (Use the #ssl command instead of #session.)
TODO: Add information about proxies and tunnels for phones and other operating systems.