ehh ... Otto I conquered Denmark in 950 and made it a vassal state (and forcing Harold Bluetooth to convert to Christianity) and in general peddled Christianity quite hard in an attempt to stop the state sponsored piracy (to go Viking) ...
You had tentatives, and succes of Christianisation since the late Carolingians (Anschaire, around 850 for instance)
For Harold Bluetooth, it was what prevented him to do as Haakon (or that any defeated Scandinavian leader that had to convert after a defeat) and to renounce to his new faith : that Christianism was already established structurally in Jutland.
that HRE control of Denmark was lost again three decades later around the time of the death of Otto II is just a historical twist.
HRE never had a real control of Jutland to begin with : it was why they tended to have a settlement policy in the region (that failed quite quickly).
In fact, as the bishops of Danemark (that, again, were already established) had to sware alligeance to the newly christened Harald, they ceased to be imperial vassals (I'll concede that as Bremen metropolitain had his seat in Imperial territory, Germans still had an hold there).
The simply fact (that you underlined) that Sven welcomed british clergy, shows that Danish kings pursued a policy of independence towards Germany (and its clergy).
The Christians pay more taxes to the state, but pay less taxes overall.
Not really. It was quite customary to make Non-Muslims pay both dhimmi taxes and the taxes technically reserved to Muslims since the VIIth century.