There is a very short way to describe this.
If you believe in an innate inequality, as opposed to egalitarianism, you are “right” wing. There is a package of various political beliefs associated with this, some of them include an advocacy for free market capitalism (there are left individuals who advocate freed markets as well, but they reject the kind of strong private property and hierarchy we propose), nationalism and a strong military/police force.
Conservatism is all about the old, it’s a reactionary philosophy. It is an opposition to risky and dangerous political, economic or cultural changes, while in favor of retaining the social order before it’s lost completely. Many conservatives may disagree on the era in which the last most successful model of society can be found, this is where you’ll find disagreements among traditional conservatives, paleoconservatives or neoconservatives.
I don’t think anti-statism is at odds with right wing conservatism. If our goals are to retain our cultural identities and promote social order then we must oppose the state. No conservative will outright deny that change occurs or that some level of change is needed, we all have individual preferences after all, but there have been many changes in our history that have had terrible effects on our society.
If you are a conservative who still feels the cultural impact the state has had on our culture is still too enormous to write it off, then try to understand that at the core of any society is law. Does the state operate on the legal principles that the rest of society does? The answer is no, at all times the state is in direct opposition to the culture itself. I hardly think any conservatives will admit a positive appreciation for communism, even though it has had a strong impact on modern culture.
The essence of conservatism relies on law finding institutions, they are reactionary. Law making institutions are necessarily radical.