Hah, well, that'll definitely require different skills and procedures than what I used to arrive at a good figure for the LDS population. What I did was take historical membership growth rates
from Wikipedia (the statistics are based on legitimate sources), and then, every year there was an uprising, rebellion and so forth, I gave them a population contraction rate similiar to that of the year 1857, the worst year of the Utah War. 1858 of that conflict also saw fighting, but it petered out, and there was a time of no growth at all as the Church entered an era of reconstruction and occupation.
So, in 1881 during the Mexican War, the Church contracts like in 1857, and in 1882, the Church's numbers remain mostly static as in 1858. In 1915 it contracts a little more severely than in 1857, and grows even less in 1916 and 1917, to account for a more harsh immediate occupation. However, 1941-1943 sees membership flight every year similiar to 1857, and another two years of no-growth afterwards. This brings the 1950 LDS membership to about 400,000. Now, the continuation of polygamy is likely to cause some changes with conversion rate and so forth, but, looking at growth patterns, the LDS Church didn't really change its growth rates all that much after giving up polygamy. Maybe since the Church is made illegal and its leaders are executed that would effect its growth as well, but in the 1880s when the LDS Church was basically made illegal in OTL, and its leaders were imprisoned for polygamy, growth rates didn't change too much either.
If I took the extreme course of action and halve growth rates from the end of the Mexican War and the involved Mormon rebellion and subsequent occupation by US forces, then there's less than 200,000 Latter-day Saints in the entire world, and I feel in my gut that's too small for the kind of things that were happening in the books. So I took the average of the two and the figure came out to 300,000... basically after the Mexican War, growth rates are a quarter less, and there is growth contaction and static growth rates when rebellion and immediate post-rebellion occupation occurs. Actually, now that I recalculate such growth rates, instead of just directly averaging the two sums, it comes out to an LDS population of about 250,000... so...
If the LDS do begin to slowly shed their poor reputation by the end of the 1970s, as stated in the alternate timeline at least in the US, then its very likely they could break 1.5 million by 2010, maybe 2 million. However, I wonder if they'll ever give up polygamy and give the priesthood to blacks. With so much more radicalization, they might not. In any case, Hawaii and the Pacific is likely to become very affected by the LDS Church. We've been in Hawaii since the 1850s and its one of our stronger areas... with the increase of a large Latter-day Saint population there, it could very well become the principal religion of the state and for that matter Polynesia.
Consider that in OTL 1950, the whereabouts of the membership of the LDS Church were Utah 50%, the rest of the United States and Canada 40%, and outside of the USA and Canada 10%. That composition could have changed considerably with so many disturbances in Utah, pushing Latter-day Saints out of the state, out of the country, for example, but also getting rid of Utah missionaries which are the principal force of growth outside of Utah and North America. I don't know where it'd all balance out to. But let's just say that half of the remaining 250,000 LDS members are in Utah. In Operation Eagle Claw, some 121,000 LDS members are moved to the Sandwich Isles. They join some 9,000 native Hawaiian LDS members (well, in OTL there would have been more than 35,000 but...). 4,000 "secret Mormons" remain in Utah. Now, Hawaii has 130,000 Latter-day Saints out of a 1950 population of (with new relocated LDS included) about 620,000. That means more than 20% of the Sandwich Islands are now Latter-day Saint. Hawaii was only 5% Latter-day Saint as of 2007. Big changes for Hawaii.
Until the 1930s in OTL, when the LDS population began to reach three-quarters of a million, the Church leadership advocated immigration to Utah and the "Mormon Corridor" in order to bolster the Church. Now, in TL-191, that kind of quota will only be met in the 1980s. Until then, from the late 1940s on, the leadership of the Church will likely encourage immigration to Hawaii and Polynesia, though that might not matter to the US government. In any case, we might assume until the 1980s demographics similiar to the rest of the history of the Church, only with Hawaii/Polynesia and Utah/Southwest USA swapped. 50% of the LDS membership in Hawaii/Polynesia, 40% of the LDS in North America, 10% elsewhere.
So by 1980, when the LDS Church is about to break 600,000, Hawaii could have 270,000 members (90% of the LDS pop. in Polynesia). And +260,000 people. 22% of the pop. is LDS and the percentage is increasing. Just under the percentage of Idaho in OTL. By 2010, assuming peace and little shift in demographic trends, there could be 1.5 million LDS around the globe, with 30% of them in Polynesia, a membership of 400,000 living on the Sandwich Isles out of a total of 1,670,000, about 24% of the population.
You definitely want to account for this divergence of Hawaii and Polynesia. Politically, economically, socially, it would be pretty important.