While sometimes unfortunate it is often necessary to have data silos that share data. The Extract, Transform, and Load (ETL) pattern has been around for a long time to address this need and there are tons of solutions out there. If you just need a quick and easy way to copy new & updated records in Salesforce to an external data source, a simple Heroku app and Salesforce Workflow might be the quickest and easiest solution. I’ve put together a sample Node.js application for this: https://github.com/jamesward/salesforce-etl-mysql
Check out a demo:
Let me know how it goes!