Because you're not there for 'the society'. You're their for the people. Each of which has a list of rights that you need to watch like a hawk to provide and defend against the society.
It is not hypothetically impossible that Amishism is one of the most desirable ideologies in the star cluster/galaxy/universe/multiverse and that it will become bigger and bigger as individuals flock to join it, that's true. It is, however, incredibly unlikely. Much more likely is that it's devoured by ideologies that were built for and adjusted to more advanced living conditions and so can better get converts.
However you think not having the PD will go, it shouldn't be treated as, 'Oh the native culture will definitely be fine after having all it's fundamental principles changed.'
As for my point on birth rates, population growth is not infinite and we should treat it as having a 'cap' for this discussion. Otherwise you have a situation where the spaceAmish on the back of a napkin somehow fill the entire universe in a few generations because that's how ridiculous things get with a few generations of exponential growth.
So the 10%+ leaving rates would functionally obliterate spaceAmish communities that have hit their population limits in a few generations. That is hardly 'preserving culture'.
That's true, but it's also not what people mean when they say, 'native culture'. It's a whole system and way of doing things.
For example, I love eat sushi and teppanyaki and I watch anime. Does that mean that if Cloakieism becomes the predominant culture on Earth, that Japanese 'culture' has 'survived'?
I don't think so. I think it would mean Japanese culture is dead but had good food and an effective art style.
You have no right to the company of other people. If your society decides to shun you, they have the right to do so. That's what "free association" means.
I also don't think that the Amish will grow to populate whole worlds in an imaginary future where humanity spreads across the stars, but I don't think I can predict the future. The odds are that we stay right here on Earth.
Christianity and Islam were born under radically different conditions that those of the present day. Christianity and Islam still exist. People still convert to religions which were born hundreds or thousands of years ago.
All of your space predictions are largely irrelevant, because we're nowhere near colonizing space. Since we aren't moving off Earth in any significant numbers in the near future, you're trying to predict the far future. If you've ever read any science fiction stories from the early 1900s, you can see how unreliable that is. We don't all have robot butlers and personal spaceships, like many people thought we would by now, so I wouldn't count on your ability to see what the future has in store.
Whatever the future holds, it will not be uniformity of the sort that you imagine. We will not be freed from the dead hand of history, and our families and our communities will continue to shape us. There is no "New Soviet Child" liberated from the shackles of the past, as you spoke of in one of your first posts. We are all the products of our environments.