I have the same problem again, just started a few weeks ago. I've had this happen a couple times in the past, and it always went away on its own.
I'm not on the beta, just regular watchOS 4 on a Series 3.
Some people on the Apple discussion forum think it might have to do with using theater mode.
I tried a few things this weekend to no avail:
- General > Reset Sync Data
- Unpair and restore from backup
- Unpair and set up as a new watch
- Set up my old watch again (Series 0)
- Deleted completed reminders
- Created new Reminders lists (both local and shared)
There's a workaround on the Apple discussion forum. If you want to add milk to your shopping list, you would say "Add milk to my list" and then Siri asks you which list to add it to. You can select the shopping at list at that point. Not perfect, but at least you can use just your watch.
I suspect it's a server issue, since it randomly goes away and doesn't work on my other watch either.