This topic seems to me to be one of the most impossible facing both orthopraxy as a group (movement?) and orthopraxers as individuals. If it will stand as a group/movement (groovement?), orthopraxy should know if it will attempt to be passed down to children, or if it is only a transition stage for those who have lost their belief. Individuals, meanwhile, must face the question: what on earth do you teach children, and how do you raise them in an orthoprax home?
The options, as they appear to me:
1. Try to teach orthopraxy directly--no beliefs taught, but "these are the practices we do, just because this is what Ortho(something) Jews do. It's our community and lifestyle." This seems to get sticky, however, when getting into the cognitive dissonance of traditions like brachot and prayer. ("No, we don't believe in the God of Abraham. Now stop asking questions and go daven Shemoneh Esreh.") Or, when the child gets old enough to understand what Orthodoxy is, and wants to do things Friday night.
2. One parent is orthoprax, one orthodox. The orthoprax one stays quiet and lets the orthodox one do the talking. Perhaps this could actually work for some who don't care much or aren't strong disbelievers, but not a great idea in my view. People need intellectual honesty in their lives as best as they can reach it.
3. Parents recreate their exact life experiences by perpetuating a "noble lie," teaching orthodoxy until the child reaches a certain age. Then, they sit the kid down and reveal that it has been a lie, but the kid is now too emotionally/communally invested to walk away. A repulsive idea, of course, but I include it to point out that, quite frankly, it's the only actual way to perpetuate the orthoprax experience. Orthopraxy is a weird lifestyle, what can I say.
4. A more sensible combination of 1, 2, and 3: orthodox beliefs are taught just in the way many innocent beliefs are taught to or maintained for kids, in a light, left-wing MO manner. (There wasn't much focus on belief in my MO upbringing, now that I think about it--that was when I got to yeshiva.) As they get older, more and more serious age-appropriate discussion about the world ensues.
So, more or less normal LWMO upbringing, but parents will step in to undercut something taught in school if it's past a line to them, and get the child thinking critically about religion at an age-appropriate level.
5. Parent(s) is/are orthoprax, but raise kids more or less Conservative, coming to terms with an ebbing away from orthodoxy. Traditions are kept in the home for traditional reasons, but with greater flexibility than the parents' upbringing would allow. Jewish education is more or less Conservative, and children are given the freedom to do what they would like with the traditions with which they were raised.
Did I miss any?
Of these, #5 seems to me by far the most sensible, but I can see how for some people more invested in orthodoxy, #4 would be more realistic. #5 would mean orthopraxy is not really tenable as a movement for more than a one or two generations. Perhaps that's a shame, perhaps not. Either way, is there a better option?