First of all, the "hard drinking" rebels that founded the country called themselves "liberals." Even the fundies amongst them, like Patrick Henry were not "conservatives" of the time. The "liberal" fundies and rationalists that founded our nation embraced the radically "liberal" notion at the time of toleration of all religions--fundie and otherwise.
The conservatives at the time of the founding were loyal to old political ideas of the time like monarchy and a state church.
At the beginning of the 20th century, the meanings of the political terms "liberal" and "conservative" reversed themselves with regard to fundie-religion. The hard drinking "conservatives" like Mencken opposed the "liberal" church lady prohibitionist reformers.
Sometime during World War II, the next group of Americans to call themselves "conservatives" re-adopted fundie religion, empire, and declared war on communism.
The last good Americans to call themselves liberals were around at the time of the founding and the last good Americans to call themselves "conservatives" were around at the turn of the century. Hence, the terms "classical liberal" and "paleo-conservative.""
The issue isn't what labels we put on people, but what they believe. John F. Kennedy would be a conservative by todays standards. The founding fathers would be homophobic, extreme right wing nuts on the FBI's terrorist list.
I'd suggest that opposition to communism was the one thing that happened to unite paleos with all the other "conservatives" during the Cold war. Note the resplit and disconnection of conservatives today after Reagan and the fall of the Soviets and recession of communism. Many paleos did become ardent cold warriors. The cold war was a temporary, necessary and pragmatic alliance. A long strange ride we were on. The ride is over and the alliance has ended.