J,
I encountered this a little with my mother ("You sound like you're joining a cult!") and she's a freedom-minded person herself. I, speaking from experience, humbly submit that part of your parents hesitation may be a reaction to your own zeal regarding FSW. If you're excitedly talking about signing a statement of intent (which to your parents may look like a contract) and then about how all these like-minded people are congregating in a certain area (sounds like a compound) and there's this cool guy who calls himself Boston T. Party who said this, this and that (cult leader!) then your parents may be misinterpreting the FSW as some sort of super-organization that is sucking their son in.
In reality, it's an effort of like-minded people to live within the bounds of the same state and hang out once in a while, while working on some political activism. It's no more a cult than your parents church is a cult - and even less so, in fact, as there are no religious connotations. (I say that as a Christian!) Are the Boy Scouts a cult? People who have car or motorcycle groups and go on weekend trips to the mountains? Gun clubs? The local Republican Party?
Your parents are certainly concerned that you'll be moving directly from under their wing to what they see as some organization that is going to "take you in." I think what they're failing to realize, and you may try to convey better, is there are few organizations that will encourage you to be as independent as FSW! You're not going to be able to camp out at one of these folks' house indefinitely, not working, not looking for your own place to live, etc. Sure, they'll help you get on your feet when you get there, but they wouldn't be FSW people if they liked freeloaders! If you move to Wyoming you'll be living independently - and freely, hopefully - period.
Anyway, I don't mean any disrespect at all, but after reading your question where you asked "are we free to move back out of WY" I have to admit I kind of shook my head and went "Well no wonder!" Of COURSE you're FREE to move, that's the whole point of coming to WY in the first place! I had a hard time explaining the purpose of the SOI to my mother, since she kept asking what exactly what would happen if we signed it and DIDN'T go, or left soon afterwards. I thought for a minute and said "Well, nothing." Since nothing would happen, she didn't get the point. I explained to her that the point was essentially a verbal committment to the movement, and that it's a matter of keeping your word or not. According to the SOI, you'll have kept up YOUR end of the bargain after establishing voting residence in WY - and that's all it takes! Of course, if you sign the SOI and show up, nobody is coming after you in the first place, but I take it to mean that my committment to the idea of the FSW is fulfilled after I move and vote.
So to sum all that up, you're signing a pledge, not a contract, it carries no repercussions for breaking it other than whatever value you place on breaking your word, and you are free to come or go as you please because the whole thing is, after all, called
FREE State Wyoming! If you know all that in advance and explain it to your parents (or whoever else may ask) without hesitation, explain the point of the project, explain that you won't be confined in Boston's basement eating poisoned applesauce, etc., I think you'll run into far fewer problems.

Oh, and for the record, I don't even bother explaining the FSW by name to most people. Maybe that's poor PR of me, but when people ask what I'm intending to do after college, I explain that we're most likely moving to Wyoming. When they ask why, I tell them it's because we're pretty libertarian and the state politics allow far more freedom than anywhere else we've looked into, plus we figure we'll fit in with the western/cowboy/hunting/gun culture. I mention the outdoor recreation, the low taxes, the friendly business climate, the brain drain that creates a pretty ripe place for many college graduates, etc. If the person seems receptive to all that, then I'll mention that I've met a whole lot of similar-minded folks that are either moving there or have moved there, and that it just seems like the place to be... By that point the person is either nodding in tell-me-more agreement, or looks bored and like I'm totally crazy for ever moving to somewhere like WY. The prior sometimes gets the whole FSW story, the latter rarely does. I figure why bother!

Laurel