Electrons seem to be point particles. However, if they really are point particles, then they would have infinite density, so very weird things would happen according to general relativity: naked singularities, closed timelike curves, causality violations. Do we have the ability to observe whether those weird things are happening?
Scaling general relativity down to those sizes is known to have problems (what problems?), because we lack a theory of quantum gravity.
Ignoring these problems and assuming general relativity holds at the scale of electron mass and charge, we can calculate the minimum size it can be before a singularity forms. That size is smaller than what we can currently experimentally measure about an electron's size. Therefore, electrons are not yet definitely point particles for the purposes of discussing general relativity. (They can be usefully modeled as point particles for many other applications.) If they turn out to have positive size, perhaps being constructed out of strings, the string theorists won't be surprised. Though then the problem shifts to, what are strings constructed of, and why don't they undergo gravitational collapse?
Similar questions can be asked of quarks.
Photons are massless, but they do have energy, so mass-energy. Can photons undergo gravitational collapse?
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