you're wrong to suggest that objectivity of analysis isn't worth considering
I abhor anything but objective analysis, which to me means something very close to "honest analysis." My suggestion above basically boils down to the idea that independent thinkers should read primary documents (while understanding their context).
Go read Marx's manifesto. Read Mussolini's writings on why Marx was wrong and how fascism is a better system. Read Keynes. Read Friedman's deconstructions of Keynes. Read Mises' deconstructions of socialism (particularly the problem of economic calculation). Read Rothbard's deconstructions of monetarism. Et cetera. But skip the false textbook-style 'objectivity' that just randomly assembles the ideas of history into an incongruent mush.
But that doesn't mean all approaches to economics are equally objective
Correct; I would never suggest as much. Some are logically inconsistent, or consist of arguments mired deeply in logical fallacies. Some grossly conflate cause with effect and correlation with causation. Many focus only on the benefits of a policy to a concentrated group while ignoring the diffuse costs to the rest of society. And some advocate policies that never produce the outcome that is promised.