This type of premise (which comes up too often) is fairly absurd. OK yes European conservative parties aren't viciously anti-gay, aren't full of people who believe the Earth is 6000 years old, and don't have much of an NRA element. That doesn't make them appealing to US Democrats unless these people are single issue voters. You seriously think most US Democrats would be inclined to support the party of Thatcher?
In addition its worth noting that European conservatives aren't any better than/are arguably worse than the Republicans in regards to xenophobia.
Spot on. Two Thatcherite parties and classical liberals (that are right of CDU) are not the centrist option, no matter how much deluded right-wingers wish them to be so.