As far as my knowledge of the viking sttlers goes they behaved in a very similar to the Moors in Spain.
They came, they conquered, the settled and then they let people prety much carry on as usual. Dublin was just a trading post for them really that they commanded.
No religion was imposed. No lifestyle changes were enforced except for 'you must sell/trade with us.
From what I know they didn't really travel much inland nor did they mix in ... erm ... a genetic way.
I believe this to be he case in many other parts such as the Scottish islands. I remember the same being said of York too.