"just"...
In humans, even a small loss in genetic variability such as cousin mating 1.5% is bad enough that we have laws against it in nearly every society.
Charles II, the last Habsburg king of Spain, had lost 25% genetic diversity and was mentally and physically disabled, and infertile. This genetic loss is equivalent to parent-offspring or sibling mating.
Some animals, like lab mice, can survive without genetic diversity, but they are much less fit and difficult to raise. Your half clone would have lost nearly 100% of its genetic diversity. A near-full clone mechanism exists which would preserves genetic diversity. We'd have to sequence this shark to find out.
I thought this sounded suspicious, so I looked it up, and it's not true. Cousin marriage is legal in all of Europe, Australia and New Zealand, South America, Canada, Mexico, the Middle East, Russia, and India.
In The USA, cousin marriage is allowed in 17 states. But 40 out of the 50 states allow cousin sexual relations and cohabitations.
The only places in the world that cousin marriage is illegal is in China, Korea, Japan and some states in the US.
Whatever you think of cousin mating, it's just not true that "we have laws against it in nearly every society." In fact, just the opposite, it is allowed in nearly every society.
An organism may end up with 2 copies of a defective gene and demonstrate problems. However, having two working copies of the same segment is not a problem.