[JumpCrisscross]

Is it just charge that causes particles to have an antiparticle?

[pfdietz]

No. Neutrons and antineutrons are different particles, for example.

[lanna]

Neutrons don't have charge, but their quarks do. Antineutrons have quarks with reversed charge.

Just like a neutral atom can have a neutral antiatom.

[addaon]

If you prefer, then, neutrinos are neutral but have an anti-particle (although it's still possible that neutrinos are Majorana particles, in which case they're their own anti-particle).