This is a complex topic, and I don't have time to go into that much detail. I wanted to make a few points for clarity.
First, it's worth noting that I've also described liberals, or progressives, or leftists in other articles, and these were accepted even though there are probably many self-identified liberals who don't believe all of the same things. But these are acceptable because we aren't just declaring a bunch of people to have a belief. We are focusing on a particular cluster of beliefs, using the common label, and discussing withing that context. I'm doing the same here. Yes, if we stretch the term conservative to mean anyone and anything, then no statement can be true. But that's not the purpose. We aren't trying to slander some people by association with others. We are trying to identify the root ideology and the implications of that ideology.
This is true for liberals, libertarians, and conservatives. For the most part, these are not just people who randomly picked a bunch of political conclusions. Each group shares some fundamental assumptions that leads to a cluster of political conclusions. Conservatives, as diverse as their backgrounds are, are surprisingly uniform in their political conclusions. Same with liberals. This is either a huge coincidence, an extreme case of peer pressure, or because there is some philosophical foundation that leads them to these conclusions. I believe the latter.
Further, conservative intellectuals have gone further and described their intellectual assumptions. One of the clearest views comes from Thomas Sowell in "A Conflict of Visions" and others. But there are plenty of others. These are not just vague statements like "smaller government". They include metaphysical, epistemological and moral assumptions.
1.) Imperfection of man. Conservatives view man as imperfect and prone to immorality. Morality needs to be encouraged and immorality discouraged.
2.) Non-adaptability of man. Conservatives view man's nature as fixed, and distrust leftist schemes to try to reshape society.
3.) The Invisible Hand. Morally worthwhile benefits can happen when selfish desires are turned towards social benefits.
4.) Spontaneous order and the wisdom of tradition. They accept that lots of people making little changes over time can lead to better results, even though it wasn't planned. Consequently, they see institutions and traditions as a kind of inherited wisdom from the past. Since they weren't planned, we don't know all of the reasons they are the way they are. We don't understand all of the good that they do. So getting rid of them, or making substantial changes to them, is foolish.
5.) The limits of reason. The spontaneous order and decentralized decision making leads to a kind of institutional wisdom. No one person can be aware of the countless reasons why the institutions or traditions evolved the way they did. So counting on someone to use reason to figure these things out is stupid and dangerous. It's central planning vs. free-market. The central planners, no matter how much knowledge they have, are completely ignorant in comparison to the decentralized knowledge of the market.
6.) Checks and balances. While leftists think of themselves as morally elite and therefore should rule with absolute power, conservatives view man as inherently corruptible and we should always put limits on them.
7.) Altruistic results. Conservatives differ from liberals in that conservatives are more interested in results and not just intentions. They are willing to utilize things like the free-market to direct selfish impulses towards socially beneficial results. In fact, since they view man as prone to immorality, one of the primary political goals is to shape the incentives towards moral results.
There's a lot more, but this gives some sense of the philosophical foundation. Note that I'm not simply dismissing conservatives as religious nut-jobs, or complaining only about their social conservative tendencies. These philosophical beliefs are not necessarily tied to religion (although religion can emphasize or support some of these).
But these beliefs do lead to a cluster of political conclusions. They support laws that strengthen moral results, such as anti-gambling or anti-drug laws, as well as laws that strengthen marriage or provide tax incentives for charity or having children. They are more respectful of traditions like Senate rules, and the rule of law. They favor smaller government, because of the imperfection of man, but they strongly support some forms of government intervention as long as those satisfy the wider goals of promoting morality through incentives. And much, much more.
All that being said, it's a mistake to assume that because people accept certain conclusions, they share the same reasoning or assumptions. Just because conservatives seem to be for the free-market and smaller government doesn't make them libertarians, or even libertarian in those areas. Their reasoning is different.
Take a certain kind of libertarian, admitting that it might not be inclusive. One kind is the political individualist. Each person lives amongst others, but they are living their own lives. The goal of politics/government is to allow each individual to live his life free from the interference of others. An individualist libertarian may support the free-market, but primarily he support the freedom of individuals to act on their own. Free-market isn't supported because it leads to prosperity, or because it focuses selfish desires into socially desirable ends. These may be a nice effect for the libertarian, and one that he can appreciate, but not the basis of his support. Freedom is the politcal goal.
This is a huge contrast with the conservative philosophy. Conservatives are not primarily individualists. They are altruists, and consequently collectivists. They don't support each individual's right to live however he wants. They support freedom as a means of achieving altruistic goals. But it's always "freedom with responsibility", which means freedom with limits. You are free so long as you avoid certain kinds of choices. You can start a business and be a billionaire, as long as you don't price gouge or hire immigrant labor.
In comparison to liberals, conservatives often seem to be speaking a language that libertarians understand and recognize. But clarity comes from looking at the disagreements and understanding when agreement is superficial. Some people are shocked when Republicans gain power and instead of shrinking government or increasing freedom, they focus on a socially conservative agenda. But that should only be surprising to those who mistook agreement on certain conclusions as agreement on key beliefs. Priorities will obviously vary significantly based on the actual beliefs.
None of this has anything to do with some political strategy. I'm not interested here in trying to no offend potential allies because they are closer to my political conclusions than others. My goal is to seek clarity. To understand how their beliefs are different, and to anticipate where their different philosophical beliefs will result in different conclusions. The same can be done for anarcho-capitalists. Some would say we all agree to have smaller government, and we're far from that, so who cares about that last little bit. But the philosophical assumptions lead to different conclusions. We already see conflicts on that front in the area of foreign policy.