The truth is that right vs. left don't aptly describe
conservative. Conservativism properly is an attempt
to hew to the older standards and views. In the 19th century, there was no question that this centered
on authoritarian rule in most countries.
In the US, it was better aligned with classical liberal laissez-faire principles.
One problem though was (and this is the true curse of conservatism) things changed. So, in order to
remain relevant, conservative principles became aligned with robust foreign policy, often focused on
propping up right-wing regimes (conservative in their own countries), sometimes enhanced federal
law enforcement and prosecution (a la the McCarthy excesses) Too, the laissez-faire principles, which
favored the wealthy, generated an alignment between conservatives and big business, which, instead of
being quite so laissez-faire, started incorporating legal structures and mechanisms to tilt the playing
field further.
Liberalism also went through its shifts in meaning, but less rooted in traditional ideas. It was the negation
of conservatism. Early on, this ment removal of the aristocratic barriers, but as time went on, it included
removing wealth barriers, to give everyone a fairer shake. The first was a breaking down of state limitations,
whilst the latter was creating new ones.
One must live with how the labels evolve though. And that evolution includes seeing the facists as right wing
despots and the communists and left wing ones - based largely upon whether they support the existing structures
of wealth and power, or seek to create a new one.
Until recently, there was little sign of any strong tendencies toward a political move toward either flavor of
authoritarian rule in the US. MacArthur, Long, and some others embodied certain aspects, but never garnered
the support to lead a major party. Maybe Nixon came closest, seeming to believe he was above the law, but
he didn't tend to brag about it outright.