I know that many religious groups moved to America during that time, but how else were they affected? Did the different colonies choose sides i the conflict, or did they generally just not care because they were an ocean away?
This was asked recently and this was my response in that thread. It focuses on Virginia and Massachusetts, so maybe someone else can fill in info on the other colonies of the time (which were admittedly small in the 1640s-50s):
Both Massachusetts and Virginia tried to stay neutral, so as to preserve their livelihood of shipping fur and tobacco and other goods back to Europe. However, when push came to shove, Massachusetts was a bit anti-royal so wasn't too upset to see the King go, while Virginia remained loyal to the crown.
"Virginia boasted that she was the last to acknowledge the authority of Cromwell and the first that returned her allegiance to the throne."
As for colonists returning, it's very unlikely. Sea voyages were dangerous, there were only something like 50,000 Englishpeople living in America at the time (and only a fraction of that would have been men of fighting age) so there wasn't any need for them, and most of those either owned land or else were renting land from a landowner. Leaving America to fight in a war would have meant economic disaster to them and their families, let alone death.
Sources: