Op I'm glad my post was useful. It's incredibly worrying and stressful when they won't eat! (Won't sleep, teethe, get sick etc)
I've been looking after babies since I was 13 solo and was a nanny before having dd and then became a childminder when she was a year old.
Yet in that first year at times I forgot my own knowledge and experience!
There were 2 particular occasions when I phoned my own mum in bits and then when she'd finally calmed me down (and could understand what the hell I was saying!)
Each time she ended up saying to me like "seriously?! Have you forgotten your own experience?" And then proceeded to remind me of basic tips and tricks that I DID know but had forgotten amidst the stress, sleep deprivation, hormones etc
Really basic stuff - real d'oh moments for me
It's hard to see the big picture when you're at the eye of the storm.
Mn can be great for outside the box ideas but it can be judgey and eye rolly sometimes too.
Personally I don't think they're old enough at this age to learn the "if you don't eat that you're getting nowt else" rule - there is a time and place for that and this isn't that time. Older toddlers/preschool and definitely school age can learn this one BUT remember too that she is a little person in her own right and is allowed likes and dislikes too. Just like adults. If you notice a particular food isn't liked on a long term basis just don't offer it.
My dd (now 20) also can't stand cucumber never has liked it. She also doesn't like chips or potatoes generally and doesn't like deep fried foods. Somewhat unusual for her generation 
we found out many years later it was due to these foods are an irritant to her due to a disability that wasn't dx until she was 12
I've always hated radishes, sprouts and most meat (I went veggie at 16 and started eating much more having been a "fussy" eater until that point), turns out red meat seriously aggravates my stomach (on the odd occasion I've eaten red meat or red meat byproducts since, even quite soon after I went veggie when labelling wasn't so good I've ended up seriously ill inc being hospitalised once I was that bad with d&v)
My mum never liked seafood as a child but had it pressed on her on trips to the seaside as a "treat" until one time when she took a massive allergic reaction resulting in ambulance the lot!
I'm of the opinion often dislikes indicate that food doesn't suit that person for whatever reason now and so I think we should listen to our bodies and encourage dc to do so too - but you have to balance that with not encouraging unwarranted fussiness too.
My ex was terribly fussy when I met him largely I believe because he was the youngest of 4 and his mother babied him and when he went through the usual toddler fussiness/tantrums she pandered to it with him (even though she didn't with the others) and by the time I met him there were literally 6 foods he would eat! He had major issues around eating out etc too. I gradually weaned (pun intended) him onto a wider ranging diet, got him cooking, finding recipes, eating in restaurants he would never even have considered when I met him. But man it was hard work to do that with an adult!
It's a balancing act. I wouldn't entertain "like carrots today don't like them for a week then decide I like them again" nonsense but a genuine dislike is fair enough.
Please remember it's all a phase at this age.
Sometimes hated phrase on mn but true and applies to so much
This too shall pass
My dd went through a phase while teething that the only things she'd eat were frozen carrot batons, toast, cheese and yogurt, the occasional piece of apple... very worrying but the hv reassured me that she was still gaining weight, wasn't lethargic or otherwise ill and this wouldn't last and right enough it passed fairly soon after.
As I say REALLY hard when you're in the eye of the storm...but make for great embarrassing family anecdotes when they're teens - and eating you out of house and home!! 