It would be a nice and cosy exception with the entity name and the workaround

Who are you trying to convince?
How often does it happen that you know how to fix an issue but you don't have the time to do it? A clear exception is still an exception.

to prevent people to use a dollar sign in an explicit entity name.

You are preventing it if the user works with MongoDB only.
I could create my project using CouchDB or a relational db and then decide to switch to MongoDB to discover that it does not work anymore.
At that point I have to change some existing classes.

Just wondering if you still think I should add the global configuration properties, they seem redundant if we validate and provide a nice error message.

if we go for the exception we can avoid the property, I guess.

By "ask" you mean configuration or someone coming to JIRA?

Yes, a user might ask about the exception or open a JIRA. If it happens often enough, we might soften our strategy (with a configuration or something else ).
So far nobody complained in the forum so it should be ok.