TLDR:
No, the Kernel was always machine independent and manufacturers of machines with different base hardware would be supported with adaption kits. Distributions in turn, like MS-DOS, PC-DOS or OEM versions did always include machine specific parts, driver and utilities.
With the extinction of really different hardware around 1990, the PC customized version became the only one widely available one (in retail). The DOS 4.01 distribution is (to my knowledge) the last that ever got rolled out by OEM for 'lesser' compatible systems.
As already implied, it's a story of much history - or better the difference between planned future and real outcome :)
The Question
Did MS-DOS ever drop ability to support non-IBM PC compatible machines?
No.
Early MS-DOS versions were designed and indeed adapted to run on machines not fully IBM PC compatible.
This was kept until the very end.
However, there seems to be a number of utilities bundled on later versions, that seem to not fully rely on MS-DOS interfaces for device access, most notably FDISK and later TUI editor edit.com
Well, FDISK for example was manufacturer-specific right from its first appearance with DOS 2. EDIT.COM in turn is just a wrapper for QBASIC's editor mode. So this might be more a question of whether QBASIC got adapted to lesser compatible systems. Its parent product QuickBASIC was.
This seems much more a question of what your definition of MS-DOS is.
If a manufacturer of totally non compatible machine
Often overlooked, but a machine had to have at least a basic 8086-compatible CPU mode, disk-like mass storage, terminal I/O and time "counting" to host MS-DOS, as these were the services the OS expects.
would've wanted to adapt these, was there an official way of doing it,
Yes, it was done by buying an 'OEM Adaption Kit' - with DOS 4 the name (may have) changed to 'Binary Adaption Kit' as an Infoworld Article of October 3rd, 1988 shows.
or were such utilities marked for more or less full rewrite for such cases, or were these not part of "core MS-DOS",
Both: they were not core of the OS, but delivered as source templates to be adapted.
In fact, already COMMAND.COM may be counted as utility, as it differed between MS-DOS 2 and PC DOS 2 in the way programs are started, as visible in the DOS 2 sources. In MS-DOS the exec call (Int 21h ) is handed by DOS, while in PC-DOS it's hooked and done by COMMAND.COM, a behaviour similar to DOS 1.x. This got removed in later versions, making COMMAND.COM the same over PC/MS-DOS.
or was the idea of being able to adapt MS-DOS for non compatibles dropped at some point of history?
Yes and no. As usual it's all about history.
History Fully Hits With DOS 4
DOS 4(.01) is a very special beast, as originally MS intended DOS 4 to support multitasking. After DOS 3.2 fixing up minor network issues and adding 3.5" drives, MS focused on their 'Advanced DOS 1.0', what later became known as the (somewhat) infamous MS-DOS 4.0. No further work on single-tasking MS-DOS was intended.
3.2 is as well a turning point, as it's the first MS-DOS version that got sold by MS as a consumer product. Up to and including 3.1 DOS was only available as customized (OEM) Version.
IBM in turn took their PC-DOS 3.2 and added support for their new PS/2 line to publish it as PC-DOS 3.3. Microsoft only reluctantly added MS-DOS 3.30 (!) under pressure from OEM customers, while being committed to 'Advanced DOS 1.0'.
PC-DOS 4.0 (Working title 3.4) was a solely IBM development. IBM added several utilities that were IBM-hardware only, most notably the DOS-Shell (*1) using direct screen access. Being the only user for their own software they did not see any reason to make it device independent like by using ANSI.SYS.
Again, demand by OEM customers, who wanted to offer DOS 4 to their customers, added pressure to MS, resulting in an agreement to back-licence PC-DOS 4.0. As part thereof 'Advanced DOS 1.0', or MS-DOS 4.0 as it was called by now got scrapped right after its first, limited release. Refocusing development onto OS/2, its first line, dubbed 1.x, replacing 'Advanced DOS' as the multi-tasking text-based follow up to MS-DOS, while 2.x was intended to replace Windows ... but that's another story.
This was also the point when MS-DOS turned into PC-DOS including various levels of hardware dependence.
While Microsoft adapted PC-DOS 4.0 and rewrote large parts as MS-DOS 4.01, there was no consumer version sold by MS. Only OEM versions. Including versions for 100% non-IBM-compatible computers like the 80186 based Siemens PC-D (*2). The 'OEM Adaption Kit' was now call 'Binary Adaption Kit'.
The next consumer version offered was MS-DOS 5.0 two years later. It seems to be the last where some form of OEM version has been made, beyond changing some display strings. Wikipedia names this AST Premium Exec DOS 5.0, but from the listed changes (in wiki and other sources) this looks rather restricted to drivers and utilities.
Essentially the need for custom DOS versions had ended around 1991/93, the same way really non-compatible machines have vanished. On one hand, even the last slightly-off machines like some Zenith, Amstrad or Tandy provided basic hardware compatibility at least for screen addresses and modes, while on the other hand faster CPUs and Windows as abstraction layer virtualized the last need for hardware compatibility by moving it into Windows drivers.
DOS 5 also marks the entry of IBM in the retail market with DOS 5.0.1. While IBM did adapt most MS changes from MS-DOS 6.0 into PC-DOS 6.1, development did split up again and this time for good. What happened afterwards is another story (*3).
Bottom Line
Yes, MS_DOS was, at the OS level, always machine independent, but at distribution level, with ever decreasing demand for specific distributions, it became more and more a blurry distinction with PC-specific being the last to survive.
*1 - Interestingly based on Microsoft's DOS Manager made for the less compatible Zenith EazyPC.
*2 - Although Siemens made that version available only to institutional customers with a large installed base of PC-D systems. Possibly due to the fact that they switched their PC production (mostly) to 100% compatible machines (PCD-2) based on a Tandon design in late 1986.
*3 - While MS turned it slowly into a support tool for Windows (some hacks are known to turn that back into a stand alone DOS), IBM maintained DOS until at least 2003 as such.
