I know it sounds massively patronising to say to an adult 'Have you just tried it?' but I don't think that's what chickenwire17 meant. Long post follows, sorry, just trying to get my thoughts on this into some sort of order!
When my son was a baby he would eat anything, but something went wrong when he was a toddler and he started refusing things he'd enjoyed before. I know my son and I know he wasn't doing it just for attention. He genuinely struggled with the taste, texture, goodness knows what else. I think it may be connected with a long series of chest and ear infections he had when he was tiny which may perhaps have made swallowing difficult at some point. (My daughter, who is the one with ASD, has no such issues! Odd.)
He remained very fussy for years and years (although fortunately he did eat a reasonable range of fruit and veg). I didn't push it with him. I routinely gave him a small portion of what we were eating to try, but if he did that and genuinely didn't like it he could have something else. I never wanted to make food into a big issue as I thought that would do more harm than good in the long term. I hope I did the right thing, and given that he now comes out with remarks like 'Calamari is one of my favourite things' which would have been unthinkable 20 years ago, I'm happy with how things turned out!
However, in the years since I've seen suggestions from professional people who've done research in this area that people (children mostly, but I'd have thought it would apply to adults too) can learn to tolerate and even enjoy foods if they just keep trying them over and over again. It can take 20 attempts, apparently. I imagine it works in the same way as trying to overcome phobias. You start by getting over the idea that even touching, smelling or being near them is harmful, and gradually get to the point where they are just everyday objects that don't cause any stress at all.
I wonder if I'd taken that approach with my son in a really supportive, non-pushy way if he might have overcome some of his fears. I rather doubt it, though. I suspect there's a very strong psychological element in all of this and having his mother, principal caregiver and cook, working with him on a problem that was already emotionally loaded would not have worked.
So the point I'm groping towards in this very long ramble is that I think some people with deep-seated psychological issues about fruit and veg (rather than diagnosed allergies/food intolerances) could indeed benefit from some kind of therapy, and that would involve trying difficult foods, but not just somebody waving an apple slice at you and saying accusingly 'How can you not like apples! Just bite into this, go on, it won't hurt you!' It would need to be somebody sympathetic and preferably not related to you, so it was all a lot less emotionally loaded.