MAC addresses aren't particularly sensitive, and are only available in your local network. The MAC address isn't available once the traffic leaves your local area network, although if you're using IPV6 your IP address may be based on the MAC address.
However, sometimes the MAC address is used, and embedded in the meta-data of some versions of Office products. An attacker might be able to identify you as the author of a document if he/she were to know your MAC address. This was true a number of years ago with Microsoft Office. I'm not sure if it's still the case, or if any other files contain the MAC address as meta-data of the file creator.