I’m assuming you can’t fix the web service itself or you wouldn’t be asking this question:
You might try calling the web service at its IP Address instead of its URL. Based on my very brief reading about SNI, that might bypass the error. If that doesn’t work, the link you shared has one useful possibility. Setting the JVM flag:
-Djsse.enableSNIExtension=false
would probably work. You can only do this on a non-Mendix-Cloud deployment however. Running locally, I think the easiest way to do this is to run your app from Eclipse and modify the debug/run configuration with the JVM parameter accordingly.
If that works and you’re using the Mendix Cloud, you would need ask Mendix support to add the JVM flag for you. I don’t know if they can or will do this.