The problem is with Siamese fighting fish (I've always hated the term "Betta") is that their personality can vary from fish to fish. I've kept, and bred hundreds of males and they can range from shy and timid to outright pugnacious.
The fish you want to keep them with shouldn't pose any probs...although neons could be partial to the odd nip at the fighter's tail. However, if you get a particularly nasty fighter, he may see the neons as food.
Personally, i'd find a fish shop that has several fighters in their sale tanks with other fish in....not those silly jam jars where the fish can't flex its fins, and watch the fish for a bit of time. You will get an idea of what they're like towards other fish.....yeah ok, they'll flare up at other males but watch them with other fish. You can then choose a nice placid fish which should hopefully be ok.
Good luck...my favourite fish.