ADDITIONAL SYSTEM INFORMATION :
The issue occurs on Oracle JDK 11+, as TLS 1.3 is not yet supported by previous version of Oracle JDK (I tested 11.0.6, 11.0.7, and 14.0.1) on Windows 10.

A DESCRIPTION OF THE PROBLEM :
When client authentication is enabled, the issue reported in JDK-8236039 arises. This can be tested by running the Go application attached to JDK-8236039 with switch "-A NEEDVFY", and connect to it with a JSSE client with TLS1.3 and client authentication configured.

The issue happened on Oracle JDK. I tested it with Zulu JDK without any issue.

STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
1) Run the Go application attached to JDK-8236039 with switch "-A NEEDVFY".
2) Create a JSSE client with client authentication properly configured:

SSLContext sslContext = SSLContextBuilder
                .create()
                .loadKeyMaterial(keyStore, keyStoreIntegrityKey, entryConfidentialityKey)
                .loadTrustMaterial(trustStore, trustStoreIntegrityKey)
                .build();

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
I expected the JSSE client to handshake properly with the server.
ACTUAL -
I received the following exception:

Exception in thread "main" javax.net.ssl.SSLHandshakeException: extension (5) should not be presented in certificate_request
at java.base/sun.security.ssl.Alert.createSSLException(Alert.java:131)
at java.base/sun.security.ssl.Alert.createSSLException(Alert.java:117)
at java.base/sun.security.ssl.TransportContext.fatal(TransportContext.java:314)
at java.base/sun.security.ssl.TransportContext.fatal(TransportContext.java:270)
at java.base/sun.security.ssl.TransportContext.fatal(TransportContext.java:261)
at java.base/sun.security.ssl.SSLExtensions.<init>(SSLExtensions.java:89)
at java.base/sun.security.ssl.CertificateRequest$T13CertificateRequestMessage.<init>(CertificateRequest.java:818)
at java.base/sun.security.ssl.CertificateRequest$T13CertificateRequestConsumer.consume(CertificateRequest.java:922)
at java.base/sun.security.ssl.SSLHandshake.consume(SSLHandshake.java:392)
at java.base/sun.security.ssl.HandshakeContext.dispatch(HandshakeContext.java:451)
at java.base/sun.security.ssl.HandshakeContext.dispatch(HandshakeContext.java:428)
at java.base/sun.security.ssl.TransportContext.dispatch(TransportContext.java:184)
at java.base/sun.security.ssl.SSLTransport.decode(SSLTransport.java:164)
at java.base/sun.security.ssl.SSLSocketImpl.decode(SSLSocketImpl.java:1151)
at java.base/sun.security.ssl.SSLSocketImpl.readHandshakeRecord(SSLSocketImpl.java:1062)
at java.base/sun.security.ssl.SSLSocketImpl.startHandshake(SSLSocketImpl.java:402)
        ......

---------- BEGIN SOURCE ----------
import javax.net.ssl.*;
import java.io.File;
import java.security.KeyStore;
import java.security.SecureRandom;

public class SSLSocketClient {

    public static void main(String[] args) throws Exception {
        File trustStore = new File("trustStore.p12");
        File keyStore = new File("keyStore.p12");
        char[] password = "123".toCharArray();

        KeyManagerFactory kmf = KeyManagerFactory.getInstance(KeyManagerFactory.getDefaultAlgorithm());
        KeyStore ks = KeyStore.getInstance(keyStore, password);
        kmf.init(ks, password);

        TrustManagerFactory tmf = TrustManagerFactory.getInstance(KeyManagerFactory.getDefaultAlgorithm());
        KeyStore ts = KeyStore.getInstance(trustStore, password);
        tmf.init(ts);

        SSLContext sslContext = SSLContext.getInstance("TLSv1.3");
        sslContext.init(kmf.getKeyManagers(), tmf.getTrustManagers(), new SecureRandom());

        SSLSocketFactory factory = sslContext.getSocketFactory();
        SSLSocket socket = (SSLSocket) factory.createSocket("localhost", 443);
        socket.startHandshake();
    }
}
---------- END SOURCE ----------

CUSTOMER SUBMITTED WORKAROUND :
I used Zulu JDK to compile my program, and it worked OK.

FREQUENCY : always