FumbleFingers's Ngram chart very clearly shows the overwhelming preference for "make do" over "make due" in published English writing through the year 2000. But now let's look at the progress of the phrase "to make due with" relative to its own past frequency in published writing, without reference to the competing "to make do with" option. Here is the Ngram chart for the period 1900–2005:
As you can see, the frequency of "to make due with" rises from approximately zero during the years 1900–1969, traverses some foothills during the 1970s and 1980s, and then begins ascending the flank of K2 in the early 1990s.
One simple explanation for the trajectory of this line graph during the period 1970–2005 is that a spontaneous movement has emerged among writers and publishers in favor of "make due" as a legitimate variant spelling of "make do."
Another theory (and one that I consider far likelier to be true) is that instances of "make due" have cropped up in manuscripts for decades, but until fairly recently publishers' teams of proofreaders and copy editors rooted most of those variant spellings (aka "accidents" or "mistakes") out before they could slip into a finished book or periodical. In this regard, "make due" is only a snowflake on the tip of an iceberg.
Because publishing has traditionally employed squads of editors and proofreaders to assault innocent manuscripts and force orthographic (and stylistic) conformity on them, people outside the industry have sometimes supposed that the finished products that the publishers sold reflected the near-unanimous preferences, precision, and spelling expertise of the named authors; and on the other hand, those same outsiders have sometimes interpreted variants that did slip through the process as being evidence of thoughtful, intentional, and informed dissent from the otherwise monolithic spelling and style choices of the majority.
In my experience, nothing could be farther from the truth. Most authors want to spell words and phrases the way the vast majority of their peers do, and publishers even more ardently want them to do so. But maintaining a high level of consistency and conformity is expensive and, in the Internet era—an era when readers expose themselves daily to writing that has undergone little or no editorial cleanup before being posted online—strikes publishers as being less and less important.
What happens when you spell "make do" as "make due" in an online article? If you notice it later, or if someone points it out to you, and you don't like the idea that some percentage of your readers will think that you don't know how to spell "make do" correctly, you simply go back into the article and change the spelling. No permanent harm, no foul. And let's face it: It's quite a luxury to keep a bunch of editors and proofreaders on staff just to intercept those types of problems preemptively. That's why, in the past couple of decades, copy editors and proofreaders have become the whooping cranes and California condors of the publishing industry.
The 15 matches for "to make due with" gleaned from a Google Books search over the period from 1970 through 1982 hint at the underpinnings of this phenomenon. They include unique instances from these fine publishers: the U.S. Congress (five instances); the U.S. Air Force; the U.S. Forest Service; Manpower Information, Inc.; IEEE; Business Intercommunications, Inc.; Turtle Creek Publishing Company; Rogers Publishing Company [Electrical Design News]; Balaban International Science Services; Library and Information Technology Association; and Horizon House-Microwave [Microwave Journal]. Not exactly Alfred A. Knopf; Farrar, Straus and Giroux; and the Bodley Head, is it? I doubt that any of these "make due" publishers employed independent reads of the manuscript by two copy editors, followed a cleanup read by one of the first two copy editors followed by a proofread by a third staffer. But that series of interventions was standard practice in many publishing houses thirty years ago. What we've seen in the years since 1990 or so, it seems to me, is the print publishing industry, more or less en masse, heading up Turtle Creek.
Getting back to coleopterist's question
My answer to the question "Is 'make due' now considered acceptable?" is, It depends on what you mean by "acceptable." For their own financial survival—and in deference to the lowered expectations of readers who spend most of their reading time online, where editorial standards are generally much lower than in print—publishers have accepted that they can't afford to police the content they publish with anything like the number of staffers that they once set to the task. In that sense, the publishers have voted with their budgets that variants like "make due" are acceptable (though perhaps not welcome) in their publications. As for readers, they've always had the choice of taking what they get or looking elsewhere for their reading material.
I think that you'll see many more instances of "to make due with" (and similar variant word and phrase spellings) in coming years. You may even start to see instances of "in do coarse" to balance the results out a bit. Ultimately, without the publishing industry's goon squads of copy editors and proofreaders roaming around and terrorizing manuscripts, we may finally get clear of the artificial constraints on spelling that began in earnest with Samuel Johnson's dictionary and the modern publishing house.
It will be interesting to see what emerges from the resulting freedom-for-all. If I had to guess, it would be that eventually a more-sophisticated but still far-from-human word-processing standard along the lines of Word will take over the task of spelling regulation and (inexpensively) mash everything into conformity with its programmers' views of what is appropriate, if only to make standardized commercial tracking of key phrases in published content more convenient. And people on the receiving end of the process will have to make do with the choices that it permits us.