When posting questions, it is often quite useful to include debug output. However, it sometimes include the MAC address of my laptop, router, or both.

What are the possible dangers of releasing these mac addresses publicly?

Disclosing the MAC address in itself shouldn't be a problem. MAC addresses are already quite predictable, easily sniffable, and any form of authentication dependent on them is inherently weak and shouldn't be relied upon.

MAC addresses are almost always only used "internally" (between you and your immediate gateway). They really don't make it to the outside world and thus cannot be used to connect back to you, locate you, or otherwise cause you any direct harm.

The disclosure can be linked to your real identity since it might be possible to track you using data collected from WiFi networks, or it can be used to falsify a device's MAC address to gain access to some service (mostly some networks) on which your MAC address is white-listed.

Personally, I wouldn't really worry about it. However, when it's not inconvenient, I usually try to redact any irrelevant information when asking for help or sharing anything.
