There's still a distinction between matter and anti-matter for neutral particles. For instance, the neutron and the anti-neutron are distinct, despite being neutral. They have neutral charge, but opposite baryon number. The neutron will decay into a proton by emitting and electron, while the anti-neutron will decay into an anti-proton while emitting a positron. Conservation of baryon number prevents the neutron from decaying into an anti-proton, which would otherwise make neutron sources a cheap and convenient way of producing anti-protons.
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There's still a distinction between matter and anti-matter for neutral particles. For instance, the neutron and the anti-neutron are distinct, despite being neutral. They have neutral charge, but opposite baryon number. The neutron will decay into a proton by emitting and electron, while the anti-neutron will decay into an anti-proton while emitting a positron. Conservation of baryon number prevents the neutron from decaying into an anti-proton, which would otherwise make neutron sources a cheap and convenient way of producing anti-protons.
That's because neutrons aren't fundamental particles. They are made up of (charged) quarks.