A recently updated entry in OED Online [OED Third Edition (September 2001) - fully updated; OED Online version September 2016] does not distinguish the etymology of 'mess' in the sense of
I. A portion of food, and related senses.
1. a. A serving of food; a course; a meal; a prepared dish of a specified kind of food. Also fig. Now hist. and Eng. regional (except as merging into sense 2a).
Figurative uses of this sense (for example, quots. 1570, a1764)
are often indistinguishable from the more pejorative senses 2c and
["mess, n.1". OED Online. September 2016. Oxford University Press. http://www.oed.com/view/Entry/117092?rskey=lnyOAS&result=1&isAdvanced=false (accessed September 18, 2016).]
from the etymology of 'mess' in the sense of
2. c. An unappetizing, unpalatable, or disgusting dish or concoction; an ill-assorted mixture of any kind, a hotchpotch.
or from 'mess' in the sense of
3. a. fig. A situation or state of affairs that is confused or presents numerous difficulties; a troubled or embarrassed state or condition; a predicament.
For all three senses (and others, including "3. b. A dirty or untidy state of things or of a place; a collection of disordered things, producing such a state" [op. cit.]), the etymology given is
Etymology: < Anglo-Norman mes, mees, messe, Old French mes portion of food (mid 12th cent.; Middle French, French mets dish, food) < post-classical Latin missus portion of food, course of a meal (4th cent.), spec. use of classical Latin missus, lit. ‘sending’....
Notwithstanding a variety of more or less poorly-considered folk etymologies, the derivation of the senses of 'mess' is not to my knowledge controversial. Senses I3a and I3b, for example, developed from figurative use of sense I2c, which itself reflects pejorative uses of sense I1a.