Below is the stack trace showing a deadlock reproduced when using WebView via JFXPanel in JetBrains IDE:

"AWT-EventQueue-0" prio=0 tid=0x0 nid=0x0 waiting on condition
      java.lang.Thread.State: WAITING on java.util.concurrent.FutureTask at 51c6338d
     at java.base at 11.0.2/jdk.internal.misc.Unsafe.park(Native Method)
     at java.base at 11.0.2/java.util.concurrent.locks.LockSupport.park(LockSupport.java:194)
     at java.base at 11.0.2/java.util.concurrent.FutureTask.awaitDone(FutureTask.java:447)
     at java.base at 11.0.2/java.util.concurrent.FutureTask.get(FutureTask.java:190)
     at platform/javafx.web at 11.0.2/com.sun.javafx.webkit.InputMethodClientImpl.getLocationOffset(InputMethodClientImpl.java:157)
     at platform/javafx.graphics at 11.0.2/javafx.scene.Scene$InputMethodRequestsDelegate.getLocationOffset(Scene.java:4140)
     at platform/javafx.swing at 11.0.2/javafx.embed.swing.InputMethodSupport$InputMethodRequestsAdapter.getLocationOffset(InputMethodSupport.java:67)
     at java.desktop at 11.0.2/sun.awt.im.InputMethodContext.getLocationOffset(InputMethodContext.java:285)
     at java.desktop at 11.0.2/sun.lwawt.macosx.CInputMethod$7.run(CInputMethod.java:779)
     at java.desktop at 11.0.2/java.awt.event.InvocationEvent.dispatch(InvocationEvent.java:303)
     at java.desktop at 11.0.2/java.awt.EventQueue.dispatchEventImpl(EventQueue.java:776)
     at java.desktop at 11.0.2/java.awt.EventQueue$4.run(EventQueue.java:727)
     at java.desktop at 11.0.2/java.awt.EventQueue$4.run(EventQueue.java:721)
     at java.base at 11.0.2/java.security.AccessController.doPrivileged(Native Method)
     at java.base at 11.0.2/java.security.ProtectionDomain$JavaSecurityAccessImpl.doIntersectionPrivilege(ProtectionDomain.java:85)
     at java.base at 11.0.2/java.security.ProtectionDomain$JavaSecurityAccessImpl.doIntersectionPrivilege(ProtectionDomain.java:95)
     at java.desktop at 11.0.2/java.awt.EventQueue$5.run(EventQueue.java:751)
     at java.desktop at 11.0.2/java.awt.EventQueue$5.run(EventQueue.java:749)
     at java.base at 11.0.2/java.security.AccessController.doPrivileged(Native Method)
     at java.base at 11.0.2/java.security.ProtectionDomain$JavaSecurityAccessImpl.doIntersectionPrivilege(ProtectionDomain.java:85)
     at java.desktop at 11.0.2/java.awt.EventQueue.dispatchEvent(EventQueue.java:748)
     at com.intellij.ide.IdeEventQueue.defaultDispatchEvent(IdeEventQueue.java:723)
     at com.intellij.ide.IdeEventQueue._dispatchEvent(IdeEventQueue.java:672)
     at com.intellij.ide.IdeEventQueue.dispatchEvent(IdeEventQueue.java:367)
     at java.desktop at 11.0.2/java.awt.EventDispatchThread.pumpOneEventForFilters(EventDispatchThread.java:203)
     at java.desktop at 11.0.2/java.awt.EventDispatchThread.pumpEventsForFilter(EventDispatchThread.java:124)
     at java.desktop at 11.0.2/java.awt.EventDispatchThread.pumpEventsForHierarchy(EventDispatchThread.java:113)
     at java.desktop at 11.0.2/java.awt.EventDispatchThread.pumpEvents(EventDispatchThread.java:109)
     at java.desktop at 11.0.2/java.awt.EventDispatchThread.pumpEvents(EventDispatchThread.java:101)
     at java.desktop at 11.0.2/java.awt.EventDispatchThread.run(EventDispatchThread.java:90)

"JavaFX Application Thread" prio=0 tid=0x0 nid=0x0 runnable
      java.lang.Thread.State: RUNNABLE
  (in native)
     at java.desktop at 11.0.2/sun.lwawt.macosx.LWCToolkit.$$YJP$$doAWTRunLoopImpl(Native
Method)
     at java.desktop at 11.0.2/sun.lwawt.macosx.LWCToolkit.doAWTRunLoopImpl(LWCToolkit.java)
     at java.desktop at 11.0.2/sun.lwawt.macosx.LWCToolkit.doAWTRunLoop(LWCToolkit.java:1027)
     at java.desktop at 11.0.2/sun.lwawt.macosx.LWCToolkit.invokeAndWait(LWCToolkit.java:827)
     at java.desktop at 11.0.2/sun.lwawt.macosx.LWCToolkit.invokeAndWait(LWCToolkit.java:780)
     at java.desktop at 11.0.2/sun.lwawt.macosx.CInputMethod.characterIndexForPoint(CInputMethod.java:777)

The "characterIndexForPoint" method performs "invokeAndWait"
 rom JavaFX thread:

             LWCToolkit.invokeAndWait(new Runnable() {
                 public void run() { synchronized(offsetInfo) {
                     offsetInfo[0] = fIMContext.getLocationOffset(screenX, screenY);
                     insertPositionOffset[0] = fIMContext.getInsertPositionOffset();
                 }}
             }, fAwtFocussedComponent);

which is then on EDT delegates back to JavaFX thread and waits for async result.

It seems a regression of the fix:
https://hg.openjdk.java.net/openjfx/11/rt/rev/808d535c4e15

Unfortunately, I don't have a simple reproducer. However, the deadlock is obvious from the code.