The extremes have always been moving and the centre does shift around but it generally has stayed pretty static except for a couple of pivotal elections. It shifted markedly to the left after 1945, and to the right after 1979.

The centrists would argue their beliefs/opinions are constant.

Lib Dems and New Labourites would probably also see themselves as centrist. Historically that means they place greater emphasis on personal responsibility/market freedom with regulations and less emphasis on state control / ownership. Also internationalist.

Getting into the semantics of differing ideologies but in UK terms we see what has happened to the Tories, the hollowing out of their centrists elements such as those that accept a mixed economy, international cooperation and trade as opposed to far right and libertarian right tendencies.

Well I'd rather have a reasoned debate with a centrist or old school Tory than the cult like far-right conspiracy accounts all over X. I might not agree with them, but at least we agree on a basic understanding of reality.