1. I was unaware that Hugh Laurie was a member of the House of Gyllensvard.
2.
EDIT: Isn't marrying a member of Vasa into Gyllensvard technically incest removed by several generations?
Well, it's not actually Hugh Laurie, although I do notice the similarity (Lucky also said 'Doctor House' in #nes). The picture I use for Markus is that of a real life Scandinavian royal. I'm afraid I can't see the second picture, but searching the address leads me to the fanpop website of Rashida jones, and I can absolutely assure you that Kristina's portrait is not her.
And yes, it is inbreeding, but not to a significant degree. To get measurable damage, you either need to have generations upon generations of first-cousin marriage, or brother-sister incest. Markus and Kristina are are second cousins one generation removed- Markus has one set of great grandparents who are the same people as one Kristina's great great grandparents, Gustav IV Adolph and Margareta of Sweden. In either case, their most recent common ancestor was born in the 18th century. So while they have one single set of great grandparents/great great grandparents in common, they also have 3 and 7 sets respectively that are unrelated. Keep in mind that relatedness drops off exponentially as you get more and more steps away from each other.
Genetically speaking, you will receive 1/2 of your genetics from a parent, 1/4 from a grandparent, 1/8 from a great grandparent and 1/16 from a great great grandparent.
Reaching back into my memory of second year genetics, this gives second cousins once removed a coefficient of relatedness of 1/128, or 0.78125%. Compare this to a clone (100%), a parent or sibling (50%), a grandparent (25%), or first cousins (12.5%). We can take from this that Kristina and Markus aren't a great deal more related than any two random Vinlanders.
As a general rule of thumb, second cousins and beyond are pretty much as safe as complete unrelatedness, and even cousin marriages aren't (genetically speaking) terribly bad things, unless you stack up cousin marriages upon cousin marriages for several generations, like what happened with Charles II of Spain (although he also had a whole range of incestuous stuff going on, like uncle marriages, nested double cousin marriages, and a whole other assortment of screwed-up stuff intended to keep power locked within the Habsburg family).
Anyway, the long and short of it is that yes, they are related, but the relationship is distant enough so as to make actual genetic similarity negligible.
OOC: At this point, pretty much all royal marriages are incest
Depends a bit on the branch, but yes, inbreeding is common in many situations. Royalty is a prominent one, as are small isolated villages and underpopulated islands. Other cases of truly over the top inbreeding have really resulted in serious medical issues.
I imagine that Markus and Kristina took all of this into consideration when the question of marriage popped up.