Angelfish have quite specific requirements when it comes to tankmates. And this works both ways.
First from the angelfish's viewpoint, any fish small enough to fit into its mouth, or even partly, will be seen as food. Angelfish are predators. Many aquarists have had them eat neon tetra and cardinal tetra, or try to. That's why the profile says the tetra in the Rosy clade in Hyphessobrycon are better, with some exceptions [more momentarily on this].
Active swimmers should not be put in a tank with angelfish. These fish, like discus and gourami, are sedate fish, cruising among fallen branches and plants. Having a bunch of fish dashing around the tank is annoying to say the least, and may stress the sedate fish. And stress brings on poor health, and angelfish sometimes refuse to eat if severely stressed. Game over. Active swimmers includes all danio and all barbs. Some characins (tetra) are in this group too, but many are not.
Now to the viewpoint of the tankmates. Many small shoaling fish are "playful" just like kittens and puppies; even peaceful species may decide the trailing fins of angelfish is too much of a temptation to pass up, and this causes stress to the angelfish. Even if no actual physical damage occurs, the signals sent out by such fish still stress the angelfish. More bad health.
Neons are known to become nippers in some situations, so this combo is bad from both perspectives. Some of the fish in the afore-mentioned Rosy clade seem to be OK, like the Roberts Tetra, Rosy Tetra, Black Phantom Tetra and Red Phantom Tetra. Other fish in this clade are notorious nippers, like the Serpae Tetra, that should never be combined with any sedate or long fin fish. Bleeding Hearts might be OK, but some members have had them attack full grown angels mercilessly.
Byron.