I guess they are separating Doug and Beth now (General)

It wouldn´t matter anywhere...even first cousins can get married if they want, though it is not recommended and they should get blood tests to see if any hereditary diseases are running in the family.

Caroline is not necessary a blood Spencer. We don’t know the details about whose egg the surrogate carried.

Why would Karen or Danielle needed a surrogate?
I don't remember that they ever mentioned a surrogate.
What we haven't learned until now is, who has "fathered" Caroline.

We know that Karen before had been in relationship with men, lost her virginity to Thorne, had been married once to Connor.

They didn't even say that Karen and Danielle had already been together before Caroline's birth, only that they had been a couple since Caroline was little.
___________
June 27, 2012

Katie: I'm not going to even address it. It's completely off the subject. Whatever hurtful awful things Bill Sr. said to you--
Danielle: I never met the man.
Katie: But you said you two have been together since Caroline was little,
Karen: Look, my father refused to meet her. He wanted the world not even to know she existed.
____________

Two, if they are related, they are third cousins. That won’t matter on BB.

If Caroline is Karen's daughter, then Liam is her first cousin (their parent's half-siblings). They would be sharing the same grand-father

Douglas and Beth would be second cousins. They would be sharing the same great-grandfather.

________

But yes, I don't know if B&B would care for such a distanced genetic connection.

B&B definitely does not care about "family" as long as they are not blood related, regardless if they had been "raised" as family:
Fling between
-"cousin" Ivy and Thomas
- former daughter/ former half-sister Bridget-Ridge

Actually she is. Caroline is a Spencer.

It was stated that Karen is her Bio mother and Danielle came into the picture after her birth....