Would you expect the Jython interpreter to be safe to use concurrently in multiple threads?  The more I find out about it, the less comfortable I'm beginning to feel about this.

Jython threads are basically Java threads. Have a look at
org/python/modules/ and regain your comfort.
The standard thread synchronisation module threading works fine,
and you can also use util.concurrent by Doug Lea, recommended.

In case you want to know how jython threads organize their stack
read the python manual about stack frame objects. Jython stack
frames adhere closely to standard python.