Are there green stars?

Purely theoretically, I can't see a problem with that. The colour of a star depends on its composition and temperature. The sun is yellow precisely because it consists mainly of hydrogen and also partly of helium and its surface temperature is about 6,000 °C. If we had hydrogen in a glass tube and heated it to the same temperature, it would glow yellow.

Light and its colour are caused by electron jumps from different energy levels. These levels and the specific colours of the light photons are precisely described (e.g. Balmer's hydrogen series). There are many combinations and not only in the visible part of the light spectrum. Lasers work on a similar principle — we force electrons to make a specific jump between two levels and so a photon of the desired frequency (or colour) is emitted.

That would be a theoretical view; now the practical one, I would like to say that I am not a professional astrophysicist. Stars are powered by a nuclear fusion which is the fusion of the nuclei of lighter elements. This produces heavier elements and a large amount of energy which is radiated in the form of electromagnetic radiation. This radiation has a different frequency (or colour) depending on the energy that is emitted. Light is only a narrow part of electromagnetic radiation — stars also emit infrared, ultraviolet, X-ray or gamma rays. However, nuclear fusion takes place only under certain conditions (it does not work on heavy elements at low pressures or temperatures). So there is a combination of elements, temperatures and pressures in which fusion will occur. And this combination means that the stars are yellow, blue, (ultraviolet) but not green. I am describing the "dominant" colour above — the Sun is yellow even though the light it emits contains other colours but not in the same intensity as the dominant yellow colour. This is due to the temperature of the Sun's surface. This, in turn, is caused by the energy produced by nuclear fusion, and that, in turn, is caused by the composition of the Sun, pressure and temperature.