Wherever a right-winger falls on his side of the political compass, his thoughts generally take the same shape.
Everyone struggles on occasion with understanding where others are coming from. Right-wingers more than left-wingers appear to have difficulty with it. This, I think, is why right-wingers tend to assume everyone uses the same reasoning and motives as they do. Understanding this is important to understanding right-wingers. Know a right-winger well enough, and you'll know exactly how he thinks others think—how he thinks you really think, deep down inside yourself.
The American right-winger believes, on some level, it is evil to ask the strong to weaken themselves. To stand in the way of a man with a powerful will is an offense to the natural order. The closer to the center he is, the less aware he is of this belief.
Conversely, it is both evil and pointless to try and strengthen the weak—either a weak man will do it himself, or he will wither (mainstream right-wingers are usually squeamish about facing the reality that total destruction of social programs will kill a lot of people). If you wither (die) because your struggle overwhelmed you, then you, personally, just weren't strong enough to handle them. There is no such thing as a struggle that can't be conquered by sheer will. Strengthening yourself through struggle is far more honorable than accepting help.
Towards the center, 'might makes right' appears in softened form. It may even be framed as compassion for the weak. What's so bad about asking the weak to fend for themselves, when it's fending for yourself that makes you strong? It's for their own good.
Right-wingers tend not to believe anyone will do anything without some incentive, regardless of political leaning or even religious belief.
Their popular term 'virtue signaling' is this concept in miniature. The user struggles to conceive that someone could want to stand up for the downtrodden without expectation of reward.
In the case of liberals, right-wingers believe liberals are after the political and social capital that can be had for doing and saying the correct things. What is 'correct' for liberals is racial justice, feminism, queer acceptance, and other things like that. The liberal makes noises in these directions, then gains cool new friends, some political clout, and of course the votes of women and brown people and homosexuals, who will vote for anybody who pets their special interests enough. (It's almost like voters usually vote for the things they want.)
The right-winger, a shrewd manipulator in his mind, believes liberals are the same way, doing the same things: play-acting opinions and beliefs for a selfish benefit.
Further right, simply lacking in cruelty is considered virtue signaling.
Naturally, the right wing tends to trust in capitalism, a system described in their own words as the only one which reliably harnesses the natural evil and greed of humans. If humans were good, the center-rightist sighs, then we could have socialism or communism or even a benevolent dictatorship. But humans are naturally bad. Only capitalism can put a bridle on these, our worst tendencies, and use them constructively.
The average center-rightist's thoughts on violence are the same as a centrist's: sometimes necessary, as in policing or war, but usually distasteful.
The deeper-thinking types are aware of the left's criticism of the state's monopoly on violence, but disagree that this is entirely bad. They say abuse of a system does not mean the system itself is worth dismantling entirely. Few have a desire to see a return to Wild-West vigilante justice.
At the extreme right, they overcome the debate between justified and unjustified violence entirely. To them, violence is neither good nor bad, but a force of nature. One described it to me as elemental in the universe, like oxygen or entropy. Another described it as a tool for useful ends, like a hammer and nail. Violence used to exert one's will is always good—violence used to crush the strong and unfairly elevate the weak
Most people across the whole political spectrum will, at some point, use appeals to nature to argue why their ideas are correct.
Some of these arguments are more valid than others—it is, apparently, scientific fact that humans need some amount of sleep every day. Anyone seriously trying to argue that 24-hour workdays should be allowed would be met with a lot of links to papers about the amount of sleep we need to function properly. (Outside of certain libertarian forums, I have never heard anyone try to argue that 24-hour workdays should be legal.)
However, right-wingers mistake things of humans for things of nature or God, so what he thinks is 'natural' is often a social construct less than 400, 200, 50, 30 years old.