Birth of a star. Now in order for a star (or proto-star) to be born, there must be nuclear fusion th

Yes, electrons do matter: they are needed to maintain electric neutrality of the matter. Without them repulsive electrostatic forces between protons would not allow formation of dense objects. But the temperatures at which the nuclear fusion occurs are too high for individual atoms, instead electrons and protons become unbound forming fully ionized plasma. On average, the numbers of electrons and protons in such medium are the same, maintaining net electric neutrality.
In the Sun, during the proton-proton fusion two protons fuse into deuteron (a nucleus of deuterium containing one proton and one neutron) also producing a positron ($e^{+}$, an antiparticle counterpart of electron) and an electron neutrino:
${}_1^1\mathrm{H}+{}_1^1\mathrm{H}\to {}_1^2\mathrm{H}+e^{+}+{\nu }_e+0.42\text{MeV}.$
Positron subsequently almost immediately annihilates with one of the plasma electrons producing two gamma rays:
$e^{+}+e^{-}\to 2\gamma +1.02\text{MeV}.$

The electrons are present in the star's core, but no longer bound to any individual nuclei. Fusion depends on how nuclei collide with each other. By the time the nuclei (also called ions) have gotten close to each other before a potential fusion event, the electrons have relatively little influence. The electrons also have about 2000 times less mass and are moving much faster, so even when an individual electron does get close to an ion, it doesn't stay close for very long and doesn't impart much momentum compared to an ion vs. ion collision.
So, electron vs. ion interactions do affect some plasma waves and behaviors, but they can be ignored when considering individual fusion relevant collisions between ions.