They're inbred already. They rarely fully accept new converts from outside of Utah into positions of authority. The LDS church is in the beginning of a death spiral. Only cultural Mormons are considered for promotion to authority status. So the gene pool is shrinking.
Outside of Utah, the Mormon church is just a curiosity. Go to Boston or New York City, and ask people what they think of Mormons. They picture pioneer women in long dresses trekking across the plains.
Most of my local ward is about as far from inbred as you can get. Most of them are foreigners who have not been born or brought up in this country and come from several continents. To give an example, we have Rastern Europeans who are married to Latin Americans and southern Africans who are married to Asians.
On the rare occasions I have shown face, I don't even recognize some of them due to the high turnover and nomadic nature of the congregation. Some people turn up, get the church to pay for their transport, electricity and rent and then move off somewhere else.
Even the locals who marry locals rarely marry within the church.
There is no danger of inbreeding round here, that's for sure.
I don't think that would be the case for a number of generations. There are still a lot of converts still coming into the church although rapidly diminishing. Here in Tuscaloosa you have kids of converts going to BYU and marrying generational Mormons and thereby enlarging the gene pool. Inbreeding won't be a problem in the near future.
This thread seems an appropriate place to relate a story that a woman I once knew told me.
Once, when she was a small child, her mother took her to a family reunion taking place in one of the counties in central Utah, one of those that was largely populated by descendants of early pioneer settlers sent by Brigham Young.
She looked around at the attendees and in innocent curiosity asked her mother, "Mom, why are everybody's eyes so close together?"
Her mother responded, "Well, they have cars now. That's going to get better."
Mormon royalty in Utah has always been inbred. Can't trust anyone outside the circle. Certain family names are always heard. This even occurs on the local level with the same people in high positions - they change up the positions but not the people.
I'm sure it will get even worse as there are fewer people to pick from. Not as many willing to Lie for the Lord as the lies become more easy to verify via the evil internet.
In my view this is why they started the Doubt Your Doubts program. Just listen to the brethern and hang on to the BS.