I know that if an electron collides with its antiparticle, the positron, they annihilate each other and energy is released. But what happens if an electron collides with other antimatter that is not its antiparticle, like an antiproton or an antineutron? Do they annihilate each other too?
No, they don’t annihilate. The electron will scatter off the other particle, though any differences in charge will of course affect the scattering. For example, an electron and a proton could become bound to make a hydrogen atom, but this couldn’t happen with an anti-proton. Any nuclear reactions (specifically electron capture) would be affected too.
In the case of free anti-neutrons, there’s a chance the anti-neutron could decay into an anti-proton and a positron. If this were to happen during the collision with an electron, the electron could potentially annihilate with the positron.