I wrote a story about the Pilgrims a few years ago, exploring their origins as separatists, and one of the claims are read in several sources about their motivation for leaving the Netherlands is that very much disapproved of how much religious freedom existed there.

Reportedly, they feared their communities were being contaminated by religious heresies, and that their children were at risk of straying from community orthodoxy and orthopraxy.

I'm no historian, and I'm in no position to know if that actually played a significant role in their deciding to emigrate to North America, but given their religious behavior when they arrived here, the hypothesis at least sounds like it has merit.