My family went to Conn in 1630 from Salem, I think that keeping our hair intact was a more pressing concern, see Pequot war of 1637.
I’ve got a line that was there at the time, it wasn’t at all the kangaroo court of modern popular perception.
For example, a female collateral ancestor got hauled up in front of Increase Mather for killing her son with an axe. She was not hanged. She was put away. Crazy woman. Quite a few influental people descended from her, though. Several Presidents, Aaron Burr, Jonathan Edwards, etc.
Fortunately they already had the offspring which led to my dad and then to me.