I’d like to start with what for me is a sort of baseline scenario for thinking about these things. Aristotle often begins a discussion by speaking in the common way about the being of things encountered in experience; but as the discussion progresses, emphasis shifts increasingly from the original naive talk about being and things to talk about form and concepts and meaning. At this point (though not at the start) we could also begin to talk about objectivity in the modern sense. (I take it that any objectivity is always emergent and synthetic.) (See also Aristotelian Dialectic.)
Modern talk about realism and idealism is very slippery, and sometimes tends to slide in an undisciplined way between several different concepts. To begin with, are we taking the terms in an “epistemological” or an “ontological” sense? And what exactly do we mean by either of these? Then, if we talk about idealism, do we mean the mental, subjective kind that is usually only attributed in the third person to people we don’t like, or something else that is nonpsychological and nonsubjective?
I take it that the Aristotelian scenario I opened with could be characterized either in terms of some sort of non-naive realism or in terms of some sort of nonsubjective idealism. These to me are the only interesting options, and to be honest, I have some difficulty telling them apart.
I then take this as a norm for everything else. The baseline is that almost everyone wants to be some kind of non-naive realist or nonsubjective idealist, and it does not matter very much which, because the practical result is very similar.
The real work — and the interesting part — is doing what it takes to be good at either. We should aim to develop the specificity of our non-naivete and our non-subjectivism. But here again, the developed specificity of our non-naivete or non-subjectivism is far more interesting than whether we opted at the base to call it realism or idealism.
I see both Kant and Hegel in particular as aiming simultaneously at nonsubjective idealism and non-naive realism. They each differently in their own much more complicated ways work out the details, and again that is where the interest lies. Hegel adds yet another layer around Kant. I think most people see Hegel as aiming at a more ambitious non-naive realism than Kant (and perhaps a more ambitious nonsubjective idealism as well). (See also The Epistemic Modesty of Plato and Aristotle; Aristotle and Kant; Brandom and Kant; Hegelian Genealogy; Mutual Recognition.)