The GOP would probably be competitive in Eastern Europe
um, no. The communists are competetive in much of Eastern Europe.
The GOP is too socially conservative for most of the industrialized world, and socially conservative countries tend to be more populist. The US is really the only country where so many people vote against their economic issues. The only country I can see where the GOP would be a good fit both economically and socially is Singapore, and even there they'd have to tune down on the religious right since Singapore's far right government is still rather secular.
Are you channeling Opebo? You sound like it...
And the GOP would do okay in Eastern Europe. Why? Communism was imposed on a good deal of it by the USSR; only Yugoslavia independently developed communism. Therefore, most Eastern Europeans really aren't too fond of communists. Although a lot of Eastern Europe nowadays is secular, it's experiencing a smallish revival. Plus, remember that social issues are only 1/3 of the troika - economics and foreign policy also count. And the Reagan/Cold War victory could be played for a lot, on both counts. Although many Democrats did take the cold war seriously (Truman, Kennedy, and Johnson are examples), the party has since been taken over by Vietnam-era doves. This has had a net positive side effect, as far as Eastern Europe is concerned - the Republicans get the 'anti-communist' sheen. Plus, secular doesn't always equal social libertine - Romania and Bulgaria or, for a greater extreme, Belarus and Russia, are all examples.
Also, not all Republicans are social authoritarians - even non-moderates. Dick Cheney is an example of a conservative who isn't really of that bent (although his daughter is probably the biggest reason for that). Generally, Republicans from Western states would do better - a bit more libertarianism in the mix.
That said, the Democrats would be considered a right-wing party in north-west Europe. I think they might consider a handful of fruits and nuts on the extreme fringe of the Democrats (from Dennis Kucinich to Barbara Lee) as left-wing.
I actually think the 'religious' and 'authoritarian' questions are different, although they're often related. Example: Communist China, their government is secular but authoritarian. A lot of 'Nationalist' parties (ranging from the Kuomintang to the BNP to the Nazis) were authoritarian but not religious.