i don't think a rational conservatism exists anymore - as an ideology - in the US.
think back to the 50s, where you had on one side the "american dream" family, and on the other the pot smokers.
The left's ideals were "let's get high, let's drop out, who needs work man, free love".
The right's ideals were "proper education, sport health and modesty, honest work, keep the world politically stable".
[i am willfully ignoring the racism as it was happening in the 50s; americans were mostly content with segregation and not having to share their country with minorities, so "keep the black man down" wasn't high on the common man's political agenda, mostly because blacks were no competition to the wealthy south]
Over time the southern, self-employed, agrarian states got hit with not being able to keep up with education. You don't need a masters to harvest corn, mrite?
The right's ideology of freedom and self reliance turned into "m'guns will kill anyone i dont like" and "we should bomb all the nations who looks like they are bad". Money got centralized in big cities, which in turn have big colleges, which in turn breed democrats.
The left wing's ideology turned from hippy crystal-healing bullshit, into science-backed modernism. Because, as a non-partisan, what kind of factual arguments can you have against statements such as "capitalistic societies with strong Socialist policies fare better". There's factual studies that these are the wealthiest, most stable, happiest societies in existence.
Science and education have left very little to the imagination. This may be why on the left they are consistently the ones that come out with the weirdest ideas, such as the LGBT pronouns fiasco - just the product of people who canot cope with over-rationalization.
But, on the right, there is little left to argue. Gun ownership, abortion, religious rights, there's not much left that's "debatable", there is pretty much a definitive answer for all of these, and it's not even work-in-progress, it's factual to the point that it can only be denied through ignorance.
I'd be happy for you to enlighten me, so show me one thing that Republicans - and i don't mean ALL of them, a few is enough - fight for which is arguably better than their left-wing counterparts.
Let me make an example of what i mean by arguably better; modesty.
Let's say that one party wants to have laws which prohibit divorce, or nudity, or pornography. These three are things which traditionally conservatives fight against, and the left fights for. We know that excessive pornography can be harmful (if you need to go to therapy, it's bad for you), and, while i see the positive aspects of being able to get divorced, there are some obvious positive aspects to a society where more couples *must* remain married, or where the rate of new births is kept in control. It's probably not as much fun of a society, but hey, there's some good in there. Let's say, you probably would not want to encourage a full-on release of all moral laws.
So, what. What is it that the US right wing is fighting for, today, which is still arguably better than the left-wing equivalent.