https://yourlogicalfallacyis.com/no-true-scotsman
I don't think you really know what you're talking about. If I said 'No true liberal likes Mexican food!' then it would be a no-true-scotman fallacy. Except liberalism is founded in progress and scientific advancement, while conservatism is rooted in the opposite--the rejection of science and progress, focusing on tradition. A liberal who rejects the sciences is an oxymoron for those reasons. It's not a TS fallacy if the positions are contradictory--eg 'You're not a real Vegetarian if you eat bacon.'
except classical liberalism actually is traditionally placed in the center
liberalism can mean either social liberalism, which is left-wing, or social liberalism, which, as i said before, is centrist
Not exactly. I assume you mean social liberalism versus classical liberalism, or something like that. Political ideology is a 4-way system, with authority at the top, and liberty at the bottom (generally). Progress/Equality on the left, and Tradition/Opportunity on the right. A high leftist would advocate sweeping government inference to enforce equal rights for all people (like the SJWs on college campuses) while a lower-leftist would advocate for personal liberty (the rights to marriage, gender identity, religion) for all people in the eyes of the government but avoid government policies that attempt to control public opinion because that itself contradicts the nature of personal liberty.
I'd be a center-left (far-left by American standards) lower (standard by American standards) ideology that advocates for maximum personal liberty with a government that attempts to create equality through the benefiting of the less-capable.