my son , now 22, is exactly the same, and autistic. He eats fubes, yoghurts in tubes, but only strawberry ones. As he has gotten older his diet has only improved very little, he will now eat iceberg lettuce! one thing, he can now vocalise is he really doesn't like sharing plates or cutlery , he now has his own cupboard space with everything seperate, his own milk, he drinks straight from bottle, milk is good, try individual cartons with straws, mine will only drink fresh semi skimmed! he eats ketchup on anything, but only heinz, at least a bit of veg even if with sugar. i always say he really only eats beige food! my daughter is also autistic and her diet is different but still very restrictive. Its a long process, and you sometimes think you have conquered a favourite and the manufactor makes a slight change, which i can't notice and they don't eat. By way microwave snacks, where he can cook him self, burgers/pizzas etc always mean he eats as no one else handles. He will sometimes eat an apple, but only if he can use an apple slicer and do it himself, and then only a green one. you could take him shopping and let him look at all fruit and veg etc, but i would try that in middle of night at an empty 24 hour supermarket!
Other things to look out for, toothpaste, and cleaning teeth, my son doesn't! sound, i never knew until they were adults and could vocalise, things like TV always had to be on a set volume number for them to tolerate sound. Touch, flannel sheets and bedding, my kids love electric throws, i think the weight of them helps reassurance, you can get weighted blankets. sock seams! mine wear inside out! and my son ALWAYS has electric fan on, comfort from feel of flow and white noise. And make sure you use same washing powder as mum, the smell and feel may be enough to throw child off balance!
I know i have strayed from food, but if you can make surroundings more comfortable, sometimes that means the child is more relaxed and will then be happier trying new stuff.