Can someone hack you if you give out your mac address?

Short answer: It doesn't hurt anything.

If someone knows your media access control (MAC) address, there's not much malicious they can do. And anything that could be done would have to occur on the same network segment, i.e. from people physically close to you on the network.

At worst, someone could "spoof" your MAC address and make it look like you are doing things on the network that you aren't. They could also use that same technique to direct a ton of traffic to your machine that could make network communications difficult (called a denial of service or DoS attack), but again, they'd have to be local to your network.

You can change your MAC address on most machines/operating systems. Most users wouldn't have a need to do that. But the MAC address that's usually used is the one that's physically burned into the chips on the network interface card (NIC). And the silly thing is, even if you did change it in software, someone could quickly and easily listen to the broadcast of it to find the new (changed) address again.