FULL PRODUCT VERSION :
java version "1.8.0_131"
Java(TM) SE Runtime Environment (build 1.8.0_131-b11)
Java HotSpot(TM) 64-Bit Server VM (build 25.131-b11, mixed mode)

ADDITIONAL OS VERSION INFORMATION :
macOS Sierra v. 10.12.4
Darwin Mac-mini-de-Oscar.local 16.5.0 Darwin Kernel Version 16.5.0: Fri Mar 3 16:52:33 PST 2017; root:xnu-3789.51.2~3/RELEASE_X86_64 x86_64

A DESCRIPTION OF THE PROBLEM :
If you need your HTTPS connection to authenticate with a client certificate, it is necessary to define a URLStreamHandler. Then, after calling openConnection you must set a SSLSocketFactory. This socket factory must use a KeyManager object with the client certificate.
So, it is necessary to cast to HttpsURLConnection, and then, a ClassCastException is thrown.

...
URL endpoint = new URL(null, url.toString(), new URLStreamHandler()
{@Override protected URLConnection openConnection(URL url) throws IOException
{
    URL cloneURL = new URL(url.toString());
    HttpsURLConnection urlCon = (HttpsURLConnection)cloneURL.openConnection();
    urlCon.setSSLSocketFactory(getMySocketFactory());
    return urlCon;
}});
...

SSLSocketFactory getMyFactory() throws...
{
        KeyStore keyStore = KeyStore.getInstance("PKCS12");
        InputStream keyInput = new FileInputStream(new File(keyFile));
        keyStore.load(keyInput, keyPassword.toCharArray());
        keyInput.close();

        KeyManagerFactory kmf = KeyManagerFactory.getInstance(
                                KeyManagerFactory.getDefaultAlgorithm());

        kmf.init(keyStore, keyPassword.toCharArray());
        SSLContext context = SSLContext.getInstance("TLS");
        context.init(kmf.getKeyManagers(), null, null);
        return context.getSocketFactory();
}


STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
Execute the test case.

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
If you apply the workaround, the test executes silently.
ACTUAL -
class com.sun.net.ssl.internal.www.protocol.https.HttpsURLConnectionOldImpl cannot be cast to javax.net.ssl.HttpsURLConnection

ERROR MESSAGES/STACK TRACES THAT OCCUR :
class com.sun.net.ssl.internal.www.protocol.https.HttpsURLConnectionOldImpl cannot be cast to javax.net.ssl.HttpsURLConnection

REPRODUCIBILITY :
This bug can be reproduced always.

---------- BEGIN SOURCE ----------
public class Test
{
public static void main(String args[]) throws Exception
{
    String sURL = "https://www.google.es";

    // If you uncomment the following line, urlCon is HttpsURLConnection.
    //URL url = new URL(sURL);

    // I redirect standard error output to null, because
    // I'm only interested in HttpsURLConnection error.
    System.setErr(new PrintStream(new OutputStream() {
                  @Override public void write(int b) {}}));

    URL endpoint = new URL(null, sURL, new URLStreamHandler()
    {@Override protected URLConnection openConnection(URL url)
        throws IOException
    {
        URL urlClone = new URL(url.toString());
        URLConnection urlCon = urlClone.openConnection();

        if(!(urlCon instanceof HttpsURLConnection))
        {
            System.out.println(urlCon.getClass() +" cannot be cast "+
                               "to javax.net.ssl.HttpsURLConnection");
            System.exit(0);
        }

        // Here I could define a custom SSLSocketFactory in
        // order to define a client certificate authentication.
        // So I would need to cast to HttpsURLConnection.
        return urlCon;
    }});

    // The SOAP call is wrong, but it is used to check if
    // the URLConnection is instance of HttpsURLConnection.
    SOAPMessage msg = MessageFactory.newInstance().createMessage();
    SOAPConnection con = SOAPConnectionFactory.newInstance().createConnection();
    con.call(msg, endpoint);
    con.close();
}

} // Test

---------- END SOURCE ----------

CUSTOMER SUBMITTED WORKAROUND :
Uncomment the line:

    URL url = new URL(sURL);

This workaround means that there is a collateral effect when creating a URL object.