The seeming luxury of having multiple words to choose from is not sufficient to offset the lingering fear that no matter which word you pick it will be the wrong one, causing people to silently laugh at you and judge both you and your grammar school teachers

I'd agree that much of the time 'not prefer' is a perfectly adequate way of conveying the same sense as 'disprefer' (just as 'not agree' will for most purposes convey the same sense as 'disagree', and 'not like' the same sense as 'dislike'). However, they aren't strictly equivalent; I might neither prefer nor disprefer Coke to Pepsi, but rather be neutral between them. Possibly the purpose for which 'disprefer' is most useful is cancelling implications – 'I don't prefer it – though I don't disprefer it either'.