Khandro
You wrote:
"The US Republican party has all my life been classed as right wing"
Don't you mean 'conservative'?
The Republicans have a right wing, but as a movement, they are conservative, not right wing, in the same way that the Tories are conservatives. There are some in the party who are on the right and some who are (traditionally) referred to as 'One Nation Tories'.
It's the same with the Republicans.
'Right wing' in US politics is the Christian Democrats.
The GOP (Republicans) have a conservative platform, with further foundations in economic liberalism, fiscal conservatism, and social conservatism.
Massive difference to being 'right wing'.