Conservatism generally follows the principle of “be conservative in your attempts to alter society”.
OpenAI is being aggressive in moderating ChatGPT, and that’s against the core principle of conservatism (at the end of the day, LLMs are taking what people say and reflecting it back, but OpenAI is adding the extra step of only reflecting some of what people say)
Re-connecting this to the reality of American politics: ChatGPT is made by a diverse team of people nucleated around San Francisco. Some people believe that the ChatGPT team is pushing “Liberal” talking points instead of the “Conservative” talking points, so they are mad.
EDIT: Since this is turning flaewar-ey and Dang is already on me about that, I suggest anyone reading this comment also read the Wikipedia article on conservatism [0].
Long story short, it's situational based on the muddy definition of "traditional," so many specific examples you bring up will probably seem to violate the above tenant (e.g., 1940's Conservatives in the Soviet Union hated free enterprise, despite Communism being a relatively new and unproven system), but given broader context, the above definition is usually pretty consistent.