America was not a single colony, but several, drawn from distinct groups within British society, coupled with cross-fertilizations with French and Spanish colonists, as well as the natives already present.

Very few (if any) recorded real-world ‘colonies’ were settled by a more-or-less monolithic group alone by themselves in ’the world'; the closest we really come in modern American history is the Mormon migration to Utah. This is kind of instructive in that the Mormon Church has maintained a very real hegemony over the state, and culturally they are quite conservative, in your usage of the word ‘cultural conservative’. This is a familiar colony trope in SF in general you have your Mormon Planet, and your Left Handed Irishmen planet and your We Dabble In Magic planet, 

Now much of that conservatism and insularity has been driven by ongoing bias and persecution (in the beginning, at least) so the group(s) that found a colony will have a great deal to do with how their society evolves.

Consider the divergence of Pennsylvania from, say, South Carolina in the early years of the United States. Some of that was driven by the differing commercial needs and products of the colonies involved, but much was produced by the differing backgrounds of the colonists themselves; Pennsylvania was originally founded by (again) a marginalized religious group, the Quakers, who welcomed other social groups to their colony, which was largely driven by trade and light manufacturing, South Carolina largely by second and third sons of nobles in England off to seek their fortune, and tended to be mainly large-scale (for the time) agricultural in nature. 

Pennsylvania needed colonists with skills and connections, South Carolina needed slaves.

Now ALL of this is intimately tied to the great Triangle Trade, which all parts of the nascent US were deeply involved in as well. This is one element that would not happen in the OTU, at least not openly. 

The motivations for forming the colony in the first place will be the biggest immediate driver of cultural evolution; as time goes on, contact (or lack thereof) with other groups will drive it after the initial few generations. “My Family has always been here” replaces “Grandpa and Grandma came over from the Old Country” in people’s mindsets.

The first thing to consider in the OTU is what, exactly is driving the formation of offworld colonies?

The outcome will be entirely different if the experience of ‘colonization’ is like 'moving to a foreign country with no people in it because they want to put you in prison for your religion back home and you’re on your own in 1700’ or ‘moving across the country to a newly built suburb in 1950’ 

Honestly, with the ready availability of inter system travel, I suspect a lot more colonies will be like the latter than the former.

You’ll still have groups that want to head off to do their own thing, but I seriously suspect it will end up like 99% of the hippie communes formed in the late 60’s, or the multitude of utopian communities founded in the late 1800’s, like the Shakers. Some of those do exist still (the Hog Farm, for example, or groups like the Amish, or Mennonites) but most disappeared or merged back onto the surrounding society.

They provide even more models of how a ‘colony’ could develop; Amish communities are essentially ‘colonies’ existing right in the middle of our existing society. 

All would provide interesting models for this kind of exploration.