I don't think the Stuarts were particularly inbred at all, probably less so than the average person, as they had wide-ranging international marriages.
Neither James I, Charles I, Charles II, James II or Anne married relatives (you might find relatives if you went back far enough, but that's true of most people who marry someone from their own country). William III and Mary II were first cousins; they had no children though, so did not contribute to the line of the family.
Pre-Stuart, Mary I and Philip II of Spain were cousins (again, no kids), taking advantage of the fact that cousin marriage was decriminalized when England broke from the Catholic church in the 1540s. Before that, cousin marriage was rare even among royalty in Christian Europe, as the medieval church banned it, although it was possible to pay large sums of dispensation and get round the rules if you really wanted to.
Royalty marrying known relatives became more common in the 18th century, because Great Britain now had laws banning members of the royal family from marrying Catholics, so there was quite a limited choice of spouses for British royals.
Historically, I don't know if royalty has actually been more inbred than the average person. Yes, they have more limited ranges of families to marry from, but they also had the option of marrying from much further afield in geographical terms than most people, so the two things probably cancelled each other out.