QM slanting anit-realist is because some prominent physicists like Neils Bohr gave the math that interpretation, and they were more persuasive than the realists like Einstein, Schrodinger, Everett.

The agnostic view is it's just a mathematical model that makes accurate probabilistic predictions when measurements are made, which says nothing about what's really going on.

Of course treating particles as points is also mathematical.

Wouldn't it be both? Electrons occupy probability clouds, but the overall probabilities of things happening are summed over the whole cloud as if, at each point, the electron was a point particle at that point?

Sure the position of an electron is not definite, but neither is that of a buckyball, but a buckyball has a shape we can describe, an internal structure we regard as extended over space, in a way that is separate from the indeterminacy of its center of mass position. This is unlike an electron, for which, if we set aside the uncertainty as to its center of mass, my understanding is that the only internal degrees of freedom it has left (in the Standard Model) are its spin and whether it is left or right handed, with no other structure to it.

It is in this sense that, AIUI, electrons are modeled as point particles.

Of course, that doesn’t mean that if we zoom in enough, probing at higher and higher energy scales, that it can’t turn out to have some non-zero fundamental size outside of just uncertainty in its center of mass position. I think string theory would say that at the string scale it would be a string.

But, AIUI, no experiment has shown it to have the kind of extent that would make it be called not a point particle (an extent in a sense beyond just uncertainty in COM position)