That is rather amusing because you can't see beyond the fishbowl. Nearly everyone in the US today believes in liberal democratic thinking.
James Burnham devised a test to distinguish liberal-progressives from conservative-reactionaries in 1965. You will find that conservatives today agree 100% with the liberal point of view on 39 of these questions. That is how successful the left has been in reshaping the values of US citizens. This wasn't true just a few generations ago.
https://www.gotoquiz.com/james...
Historically speaking, the political left advocated for equality. The right preferred monarchy, with a hierarchical relationship between people and classes and supported blasphemy laws.
K-12 and colleges teach the values of the age of enlightenment and the scientific revolution for the 17th-18th centuries. The same liberal values I am referring too of reason, equality, tolerance, skepticism, liberty, and progress. Thinkers like Locke, Hobbes, Rosseau are covered in education at the high school level as part of understanding how our founding documents.
Today children are taught that everyone is equal, that there are no "natural betters" (i.e nobility, the monarchy), and that this also applies to social class, as skin tone, sex, gender, and sexual preference. Today most conservatives would agree and will happily call the small minority who disagrees racist, bigoted and sexist. Most religous figures also teach the same, whereas they did not do so in the past. Hence, in the educational system, biological and genetic differences polite discourse and research are essentially taboo. They would also agree that segregation was wrong. Conservatives widely praise Rev. Dr. Martin Luther King and his vision.
Today, despite most still being on the books, blasphemy laws are no longer enforced, which protected the power of religions. Most don't even understand the constitution allowed for the states of have established churches, religious restrictions on office and that states even had established churches until the 1840's, with the establishment cause's actual purpose to prevent conflict due to different established state churches. Most conservatives today would not support established churches, nor would they call for blasphemy laws to be enforced.
As strange as it sounds, left and right in the USA fundamentally agree on the basic premises because as it stands both conservatives and liberals are... liberal.