There is a strong correlation between political freedoms in a given country and the level of support for the state, expressed by country's conservative political elite.
In an autocracy, conservatives are always self-proclaimed "statesmen" and "patriots", no exceptions. State as an institution is synonymous to nation as whole and critique of a government is synonymous to treason. While in a democracy, conservatives define themselves as a "small-state" party, though as the pure democracy doesn't exist, this is always tainted by a good deal of patriotic fever, resulting in the bizarre doublethink of a "conservative anarchism".
The reason for this is pretty simple. The political conservatism has always been about protecting interests of the establishment. In an autocracy, the state directly and unambiguously supports the interests of the elite, it is a tool of oppression and as such is welcomed by the powerful.
In a more open society, the state can protect political and economic freedoms and is capable to restrict the monopoly of the few. In this case, the power of establishment is expressed through other institutions like banks, land ownership and corporations. 'Small state' in this case is nothing but a code for the unchallenged monopoly of the few.
The borderline is not statism vs privatism; it is freedom vs monopoly.