I mean you'd think this would be obvious enough - but people who hate Snape bring it up as their sort of trump card. "He was so bad he was a 13yr olds biggest fear!" No. He wasn't. Boggarts don't quite work like that. Boggarts are not themselves your worst fear - they make you FEEL your worst fear. Hermione isn't actually scared of McGonagall. (I'm sure alot of first years are scared of her though I mean she is strict and stern and a little scary at first.) Did she have some irrational fear of suddenly failing all her classes? Yeah, maybe a little bit - but it is BECAUSE she is scared of not being good enough. From the first book we see her struggling to fit in with her peers. She is muggleborn, she learned she was a witch so suddenly that she poured herself into being the most perfect witch she could.
Professor McGonagall, a stern and strict witch she respects, telling her she isn't good enough despite all of her best efforts makes her FEEL her worst fear. It has nothing to do with Minerva personally - honestly it could probably be replaced with Dumbledore or someone... its just she has far more interaction with Minerva.
SO - Longbottom and Snape: How do I know that Snape isn't his absolute worst fear? Because he still attends Potions every fucking week!!! Do you think RON could attend Charms if it was run by a spider?!? He can pass Snape in the hall, he can sit in the same room as Snape, he can even be teased and bullied by Snape. His parents were tortured to insanity by Death Eaters. Severus Snape is NOT his worst fear, that's stupid. Snape just makes him FEEL his worst fear - like McGonagall makes Hermione feel hers. SO what is Neville worst fear? I think the clue comes with him quickly saying that he also wouldn't want the Boggart to turn into his grandma. Inadequacy. Neville has never been good enough. He has low self worth. The tiniest bits of praise overwhelm him. He never wins any house points and losing some devastates him. He got his magic late, his family kept trying to tease it out of him, thought he was maybe a squib. He has a proud legacy to uphold and he is terrified he cannot. He is the worst potions student Snape has ever had.
Snape makes Neville feel inadequate. His grandmother makes him feel inadequate. But mix them together... and suddenly these two very scary people that seem to have such control over his life... look a little ridiculous.
DO you think Lupin is LITERALLY scared of the moon...? Or does the moon make him feel powerless and dangerous and inhumane? DO you think Harry is LITERALLY scared of Dementors...? Or is he scared of how powerless he is against the horrible way they make him feel - the trauma they bring up from the deep recesses of his mind?
Snape was not so horrific, so awful, so scary, so mean - that he as a man became Nevile's worst fear. He, like his grandma, makes him feel inadequate.