No. Just the opposite. And Muslims in England and the U.S. often send their children back to their home countries to marry their cousins and bring them back here.
First cousins on the male side are preferred. It was intended to keep tribes together.
It's also related to the Islamic practice of mahr (bride-price), where the husband is supposed to pay a dowry to get his wife. If he marries his first cousin on his father's side, the money stays within the family.
You're also right about tribal cohesion. A wife from another tribe might produce divided loyalty in her kids.
As it points out, Muslims in the UK have about half the rate as in their mother country—which is about equivalent to Christan Arabs (half that of corresponding Muslim Arabs).