"None so blind as they/them that will not see"

Solution 1:

Picking up from Edwin Ashworth's Ngram graph, I offer the following more extensive Ngram chart for the period 1765–2008, comparing "so blind as they that" (blue lien) versus "so blind as them that" (red line) versus "so blind as they who" (green line) versus "so blind as them who" (no line because to few matches to sustain a line graph) versus "so blind as those that" (yellow line) versus "so blind as those who" (purple line):

The clear winner since about 1820 has been "so blind as those who." Narrowing the options down to "they that" (blue line) "them that" (red line), "they who" (green line), and "them who" (no line) for the period 1825–2008, we get this Ngram chart:

The results in this case are more variable (and unsettled), but taken together the two "they that/who" forms are substantially more frequent than the two "them that/who" forms. Why? I suspect that the main impetus is a reading of "none so blind as they/them" as a telescoped form of the fuller phrase "None is [or are] so blind as they/them are, who [or that] will not see." In this longer expression "they" seems syntactically preferable to "them"—especially in the instance involving "who" rather than "that," which explains why Ngram found so few matches for the phrase "so blind as them who." Early instances of the proverb prefer "they" or "he" over "them" or "him" by a wide margin.

Discussions of the expression in proverb dictionaries

As Hot Licks remarks in a comment, the proverb "There are none so blind as those who will not see" is quite old and has a tie in to a biblical text." It may also have an antecedent in the very similar expression "There are no so deaf as those who will not hear." Martin Manser, The Facts on File Dictionary of Proverbs (2002) has entries for both of these expressions:

there are no so blind as those who will not see It is impossible to make people accept the evidence of their own eyes if they choose to ignore it or refuse to believe it. ... The proverb was first recorded in the form "Who is so deaf, or so blind, as is he that willfully will neither hear nor see." ...

there are no so deaf as those who will not hear You cannot communicate with people who stubbornly refuse to listen: [example omitted]. The proverb was first recorded in 1546, with different wording (see the preceding entry), but a French equivalent was in use 200 years earlier.

Hot Licks also cites Gregory Titelman, Random House Dictionary of Popular Proverbs and Sayings (1996), which offers this entry for the proverb:

There are none so blind as those who will not see. The most deluded people are those who choose to ignore what they already know. The proverb has been traced back in English to 1546 (John Heywood), and resembles the Biblical verse quoted below. In 1738, it was used by Jonathan Swift in his Polite Conversation, and it is first attested in the United States in the 1713 Works of Thomas Chalkley. The proverb is found in varying forms: None (are) so blind as those who refuse to see; None so deaf as those who will not hear, etc. The main entry is listed in major dictionaries of American proverbs.

[Similar Bible verse:] Hear no this, O foolish people, and without understanding; which have eyes, and see not; which have ears, and hear not. —Jer[emiah] 5:21 (King James Version)

The instance from Swift's A Treatise on Polite Conversation (1738) occurs in the third conversation:

Lady Answerall. They say, she's quite a stranger to all his gallantries.

Lady Smart. Not at all ; but, you know, there's no so blind as they that won't see.

John Ray, A Collection of English Proverbs (1678) echoes Heywood in offering a version with a singular pronoun:

Who so blind, as he that will not see?

A look at some very early instances of the expression

The earliest recorded English instance of the expression is in John Heyward, A Dialogue Conteinyng the Nomber in Effect of All the Prouerbes in the Englishe Tongue Compacte in a Matter Concernyng Two Maner of Mariages (1546):

Who is so deafe, or so blynde, as is hee, / That wilfully will nother here nor see.

However, there are antecedents that express much the same sentiment. For example, from John Bale, The Image of Bothe Churches After Reulacion of Saynt Iohan the Euangelyst (1545 [?]):

In those dayes shall it not rayne vpō the wycked / they shall haue no grace to receyue the veryte. In parables and figurs shall that be hydden from thē / that shall be euident ynowe vnto the faythfull. With eares shall they heare ād not vnderstande / with eyes shall they se and not discerne. So blynde wyll their hartes be.

From Tomas Bacon, A Newe Pathway vnto Praier Ful of Much Godly Frute and Christe[n] Knowledge (1542):

These thynges be more openly knowen than y^e they nede here to be rehersed, except we be so blynde that we wyll se nothynge, & so ignorant that we wyll nothyng knowe.

And from [Here begynneth a lytell treatyse called, the (myrrour or lokynge glasse of lyfe) for co[m]fortyng of the soule] (1532[?]):

And specyally those that hath sene and loked in this foresayd Myrrour (Beat{us} qui {per}seuerauerit vs{que} ad finem hic sals erit. mat. xxiiii.) and they be so blynde that they wyll not se / nor be knowen of theyr moste fowle stynkynge deformytyes.

G.L. Apperson, English Proverbs and Proverbial Phrases (1929) finds another version of the relevant expression in Andrew Boorde, The Breuiarie of Health Wherin Doth Folow, Remedies, for All Maner of Sicknesses & Diseases, the Which May Be in Man or Woman (1547):

Who is blynder than he y^t wyl nat se.

Also from 1547 is this instance from Anthony Gilby, An Answer to the Deuillish Detection of Stephane Gardiner, Bishoppe of Wynchester Published to the Intent That Such as Be Desirous of the Truth Should Not Be Seduced by Hys Errours, nor the Blind [et] Obstinate Excused by Ignorance (1547):

There is none so blinde as they that wil not se. And seinge suche blindesse is in you bishopes, who shoulde haue had the eies to haue espied thys ware longe before it hade ben brought into the churches contrarie to the worde of God: how can it be but bi your carelesse negligence, the worlde is waxen ful of blindenesse, miserie and all kindes of ini∣quitie, for the whiche you shal answere at the dreadfull daie whan the bloude of euery one of your shepe that perisheth shallbe required at your hande.

And another very early instance of the expression without the "none so deaf" clause appears in Edmund Becke, A Brefe Confutacion of this most detestable and Anabaptistrial opinion that Christ dyd not take hys flesh of the blessed Vyrgyn Mary nor any corporal substance of her body. For the maintenaunce whereof Jhone Bucher, otherwise called Jhon of Kent, most obstinately suffered and was burned in Smythfyelde, the ii. day of May Anno Domini M.D.L. (1550):

Scripture disdaynes not, to cal Christ the sonne / Of Marye his mother, in Luke and in Mathewe, / But their hartes are so hardened they will not be wonne / They make a tush at a text, be it neuer so true. / They wyl beleue Paule no more, than a turcke or a Iewe, / To aledge them scriptures, it greately skylleth not / Ther is none so blind as they that can se, and will not.