Every once in a while, there'll be a post that says something like "Guys I just realized Percy and Annabeth are cousins." So, I'm guessing a few people are still confused on whether gods have DNA or not. I'm going to try to clear that up in this post.
I'll be using two sources to explain. Drew's explanation in The Lost Hero and a Read Riordan article.
First, here's Drew's explanation:
"“Then you’d be my half brother, silly. You can’t date somebody from your own cabin. Yuck!” “But aren’t all the gods related?” Jason asked. “So isn’t everyone here your cousin or something?”“ Aren’t you cute! Sweetie, the godly side of your family doesn’t count except for your parent. So anybody from another cabin—they’re fair game. So who’s your godly parent—mom or dad?”"
Basically, she says that only your parent counts. Not the whole godly family tree. So two demigods with the same parent can't date each other, but if they have different parents they can.
The 2nd explanation comes from a Read Riordan article. It says this:
"The godly side of your family does not count, genetically speaking. You could drive yourself crazy if you thought about it — everyone is somebody’s cousin, nephew, half-brother, uncle, or whatever. But gods are special beings. They don’t have DNA and each god is a force unto himself/herself. They pass on some of their power to their demigod children, but not the entire bloodline of the Olympian family."
This is a bit more detailed. Essentially. gods don't have DNA. Therefore inter-demigod dating isn't a problem.
There is one question I think some people might have. If gods don't have DNA, why do demigods share similar traits to their godly parents?
That's a good question. I'm going to base my answer off of this sentence
"They pass on some of their power to their demigod children, but not the entire bloodline of the Olympian family.""
I think the gods have a weird kind of godly DNA, The whole bloodline isn't given, but the traits of the parent god (like powers or eye color) are passed down.
I hope this clears up any confusion. And if you have questions, ask away