Not sure how much these terms mean nowadays, and you could even say that the left/right positioning game is identity politics in itself. Maybe it's more interesting to consider whether the ideas have merit.

Does it matter which way he 'leans'? (Hint: no, it doesn't)

Don’t think he leans any direction.

IMHO ideology is a mental shortcut where you blanket apply fixed rules instead of thinking through the specifics of the situation.

People love the various popular ideologies because said ideologies are simple and easier to understand - people want easy answers. Unfortunately the world isn’t simple.

In the words of H. L. Mencken,

“Explanations exist; they have existed for all time; there is always a well-known solution to every human problem — neat, plausible, and wrong.”

Sounds centrist, unlike virtually all those in politics.