Do electrons have no hair, like black holes?

In some sense electron's have even less hair then black holes do. Electrons are governed by quantum field theory and the Standard Model. All electrons are quantum excitations of the same quantum field. Therefor, all electrons in the universe are identical. They all have the same mass, same charge, and same spin. There is no freedom.

However, this "baldness" of the electron has nothing to do with general relativity and the no hair theorem for black holes. In fact even if you were to try to describe an electron as a classical charged black hole, the no hair theorem still would not apply to it. The electron's charge is insanely big for its mass. In geometric units, the electron charge is more than 20 orders of magnitude bigger than the electron mass. This means that when described as a Kerr-Newman solution in general relativity, the electron does not describe a black hole, but a naked singularity without a black hole horizon. The no hair theorem in general relativity applies only to solutions with a horizon.