Somewhat similarly, our ruling elite was was utterly horrified by Coulter's plan to turn Muslims into Christians with gunpoint assisted evangelism, but cannot comprehend why any Muslim might be unhappy with our current plan to turn them into progressives with gunpoint assisted evangelism.
Like them, I'm horrified at the first. Unlike them, I have no problem comprehending about the second. But I might do it anyways, perhaps for a different value of "progressive" than the one you're thinking of, on the grounds that it would be easier to get away with than genocide - if I have to. But I think a better way can be found before it comes to that.
I don't think you can turn muslims or christians into "progressives" etc at gunpoint. You can maybe turn them into wormfood.
It's cheaper and better to just buy stuff they have for sale, and help them find stuff to sell, and sell them pretty much whatever they want to buy. The richer they get the more "progressive" they'll get on average, for some value of "progressive". We don't have to do anything in particular to get this result, it's a side effect of free markets.
But I expect that will have limited results, because people generally want meaning in their lives, and US mass culture does not provide much meaning. There isn't a whole lot of meaning in being a consumer. Lots of comfortable people take up religion because they feel a great big lack.