The ideas of conservative and liberal have become very confused, and in many cases exactly backwards. Let’s try to understand them — as adjectives instead of nouns — and strip them of some connotations.
A conservative idea is one that sees value in limiting change. The assumption is that an organic system is a long accretion of wisdom or value, and should not be changed lightly. The built-up information in the system might not be obvious, and so changing it risks a greater loss than one anticipates. One wishes to conserve.
A social conservative is one who sees social mores this way. In programming, a fear of rewriting legacy code is conservative. Stare decisis is conservative. To be green is to be an environmental conservative.
A liberal idea or system is one where individuals are given greater ability to make choices. It is not necessarily the opposite of conservative.
A liberal democracy allows greater participation of citizens in choosing a government. A social liberal believes in fewer social restrictions. In economics, to liberalize is to make a market more free.
One can begin to see what misnomers these terms have become in modern politics. “Liberals” are often those on the side of greater government control. Radicals are often called “conservative”. Weird.
These ideas are not necessarily opposites, and can be complementary. For example, citizens participating in the so-called Arab spring have liberalized their political systems, but subsequently chosen conservative leaders.
One can abhor recreational drug use — a conservative premise — and understand that it should be legal — a liberal conclusion. A liberal system offers space for conservative choices.
I have largely stopped using “liberal” and “conservative” as political nouns, as they are misleading at best and pejorative at worst. Most politicians — most _people_ — are not consistent enough to be called either. It is a tribal distinction, which I find nearly useless.