I think what gets to me most with my fussy DD is that she is so averse to trying anything new in case she doesn't like it, and won't try it properly (i.e. takes the tiniest micro nibble, instantly says she hates it and spits it out) whereas if she would just eat it a few times, even reluctantly, she'd find more things she likes.
However I am quite accepting - I usually make two meals, one for her and one for me and DS, because I've learned there is no way she will eat something she doesn't like, ever - no consequence or bribery or anything has ever worked, I think she would literally rather starve - and slowly, bit by bit, she does widen what she'll eat. She will suddenly decide to try something without me pushing it, and add it to her diet.
One reason I accept it is because the things she likes and doesn't like are very specific and not particularly aligned with junk or pudding etc. She hates almost all sweet drinks and puddings, all fruit, but likes certain vegetables - so I know she's not trying to just get out of healthy eating. She just genuinely dislikes most food.
I just try to make sure, within what she likes, that she gets enough of a range of nutrients. Things that might be seen as junk, like pizza and hot dogs, are a triumph for me when she starts liking them because that means she'll get some tomatoes or protein.
She does have some ASD-like traits and that's another reason not to push it. She's very similar with clothes. We make more progress if she can change at her own pace.