I object: putting these terms in such simplistic classifications is sloppy thinking.
These concepts began Greek Mythology and literature: Apollo and Dionysus. Please read this:
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These concepts formed the basis of nearly all literature, since the beginning of time. Apollo was for order and equality, Dionysus was a free spirit, not worrying on the effects of chaos. Governments are divided on it, Churches are divided on it, marriages are divided on it, Parents and children are divided on it. Read that article.
Now, your question. In todays terms, most would put the law, order, and equality in the conservative side; however, each group uses the order argument whenever it suits them.