Eclipse Jetty 9 and Apache Tomcat 9 JAR on the same classpath

Question

Fortunately or unfortunately our application uses both Eclipse Jetty and Apache Tomcat servers internally for different purposes. All these jars are on the same classpath and this causes "Not running on Jetty, JSR-356 support unavailable" as below

INFO: No global web.xml found
org.apache.catalina.core.StandardContext startInternal
SEVERE: Error during ServletContainerInitializer processing
javax.servlet.ServletException: Not running on Jetty, JSR-356 support unavailable
    at org.eclipse.jetty.websocket.jsr356.server.deploy.WebSocketServerContainerInitializer.onStartup(WebSocketServerContainerInitializer.java:271)
    at org.apache.catalina.core.StandardContext.startInternal(StandardContext.java:5166)
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:183)
    at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1384)
    at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1374)
    at java.util.concurrent.FutureTask.run(FutureTask.java:266)
    at org.apache.tomcat.util.threads.InlineExecutorService.execute(InlineExecutorService.java:75)
    at java.util.concurrent.AbstractExecutorService.submit(AbstractExecutorService.java:134)
    at org.apache.catalina.core.ContainerBase.startInternal(ContainerBase.java:909)
    at org.apache.catalina.core.StandardHost.startInternal(StandardHost.java:843)
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:183)
    at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1384)
    at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1374)
    at java.util.concurrent.FutureTask.run(FutureTask.java:266)
    at org.apache.tomcat.util.threads.InlineExecutorService.execute(InlineExecutorService.java:75)
    at java.util.concurrent.AbstractExecutorService.submit(AbstractExecutorService.java:134)
    at org.apache.catalina.core.ContainerBase.startInternal(ContainerBase.java:909)
    at org.apache.catalina.core.StandardEngine.startInternal(StandardEngine.java:262)
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:183)
    at org.apache.catalina.core.StandardService.startInternal(StandardService.java:434)
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:183)
    at org.apache.catalina.core.StandardServer.startInternal(StandardServer.java:930)
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:183)
    at org.apache.catalina.startup.Tomcat.start(Tomcat.java:486)

Issue only started after upgrading to Eclipse Jetty 9. Removing Eclipse Jetty's JARs is not an option because we need them as well. Please help!