The commonly sold species of paradise fish shouldn't be big enough to eat neons, though they're not a great community fish because of their tendency towards aggression.
Swordtails aren't that nippy, you can get fights between males, and they're the most aggressive of the common livebearers, but they're still not as bad as some bigger tetras or tiger barbs. I had a male lyretail sword in my community tank for quite a while before he took a carpet dive and got eaten by my cat. He was a tough guy, and would bully my male platy (tried it with the molly, who took a chunk out of his tail for it), but didn't get nippy with angelfish or gouramis.
Thinkfish does have quite a few compatibility shortcomings, though. It's no substitute for more extensive research, but then, no single site can be, as there's always differing experiences, confused species, and other trip ups.