“cotton to” (eg "I don’t cottot to that idea)
If we restrict our discussion to your narrow use of the phrase, we can see
[quote=OED} 5. To ‘get on’ together or with each other; to suit each other; to work harmoniously, harmonize, agree. (Const. sometimes together, with.)
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a. of persons, etc.
1605 Play Stucley in R. Simpson School of Shakspere (1878) I. 169 John a Nokes and John a Style and I cannot cotton.
a1634 J. Day Peregrinatio Scholastica (Sloane 3150) f. 6, The draper said truth and he should cotten well enoughe.
1660 T. M. Walker’s Hist. Independency IV. 46 [The Parliament]
and their Masters of the Army could not cotton together.
1699 B. E. New Dict. Canting Crew (at cited word), They don’t cotton, they don’t agree well.
1881 R. C. Praed Policy & Passion I. x. 212 All I ask is that I may be able to cotton with the man she’s set her heart on.
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b. of things.
1567 T. Drant tr. Horace Arte of Poetrie sig. Avv, That first with midst, and middst with laste, Maye cotten, and agree.
1614 T. Adams Diuells Banket ii. 54 Our secure liues, and your seuere Lawes will neuer cotten.
1652 M. Nedham tr. J. Selden Of Dominion of Sea 163 These things do not cotten well.
1840 Lady C. M. C. Bury Hist. Flirt xviii, The vaulted roof of a cathedral..did not ‘cotton’ with lively ideas.
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that it has little to do with cotton cloth and the US South.