Oct. 9 update: I installed my new GT 1030 graphics card today and wanted to report back, mainly as a way for people to get a feel for whether or not their systems can handle 4K rips. The good news is that those with older hardware do have a shot at full 4K goodness.
First, for reference, here's my system. The only specs are the ones that, IMO, are directly related to the system's ability to play rips.
Intel i5-661 3.33 GHz processor (Clarkdale, dual core)
8 GB DDR3-1333 RAM
MSI motherboard with Intel P55 chipset
LG WH16NS60 UHD drive in a NexStar DX USB 3.0 external enclosure, and connected via a USB 3.0 port
EVGA graphics card (low profile, heat sink only) with Nvidia GT 1030 design and 2 GB RAM
Samsung SSD drive
Gigabit Ethernet connection to a Synology NAS that holds the rips
Windows 10 (fully updated)
4K HDTV display w/ HDR10 & Dolby Vision support
Was I able to play the rips? Yes, but only after I upgraded my graphics card from the original card GTX 460. Before that, the CPU would be overwhelmed by the decoding and would cause heavy stuttering. With the GT 1030, the video is silky smooth for the most part. I loaded up "Billy Lynn's Long Halftime Walk" as a test since it's 4K @ 60fps. GPU-Z shows that the GT 1030 works hard but still has some headspace (~70-75% GPU usage). VLC shows ~10% CPU usage and ~225 MB of RAM. The video for BLLHW seemed slightly jerky but I can't tell if that's an issue inherent in the source material or if it is an issue with my rig.
Regarding SSD/Ethernet/etc., it's okay to serve files on a plain hard drive, although you may want to spring for one with a faster read speed to be safe. In addition, I wouldn't recommend serving files wirelessly, at least not unless you have an 802.11ac setup that's rock solid and consistently fast. On paper, the maximum bitrate for UHD-BD is 108 or 128 Mbps (dual or triple layer), or 13.5 or 16 MB/s, which isn't much. In practice, at least with some computers, the drivers find ways to choke even when the router is next to the computer. Even BD rips can choke on my Mac's wireless setup, although that might have to do with the laptop, which is first gen 802.11ac and has always been a bit touchy.
Regarding the rest of the specs, based off VLC 3.0 memory usage, I suspect that 4 GB RAM would be a minimum on a PC but I'd recommend 8 GB to be safe. The CPU depends on whether or not there's a GPU with HEVC decoding. (I believe this is true for Kaby Lake processors and know it's true for Coffee Lake.) No matter what, you must have either a beefy CPU or a reasonably beefy GPU card in order to play rips. If using a GPU for HW decoding of the HEVC Main 10 profile (i.e., UHD BDs), I believe you'll need the following.
Intel: Kaby Lake refresh or Coffee Lake (Skylake can only handle the HEVC Main profile, and not Main 10)
Nvidia: GTX 750 SE (supposedly an OEM-only card), GTX 950, GTX 960, or any 1000-series or Titan card
AMD: Radeon R400 series or higher card (R400 series must have UVD 6.3 or higher)
I can't comment on Linux. I assume that if the GPU drivers support HEVC decoding, you're good to go, although you may have to play with settings to get the full 10-bit color. Somebody else will have to figure out the Linux setup. I also can't speak fully to Macs. I assume any Mac with a Kaby Lake processor has full support for HEVC Main 10 decoding, but again, getting 10-bit color might be an issue.
In case anybody here is curious, do not install the UHD version of PowerDVD 14 on your computer unless you have a fully supported rig. The original version of PowerDVD 14 was happy to play HEVC video from MKVs, even 4K discs. The UHD version seems to shut down all HEVC video unless you have a completely controlled path (i.e., SGX and such). Even standard-def HEVC video I made from some old LaserDisc transfers won't play on the new version. Very annoying, but thankfully, there are programs that happily play these files with the SGX nonsense.
Finally, there are other variables not discussed here, like the fact that my motherboard uses PCI Express 2.0 and not 3.0 (the latter can handle a bit more data). Things are going to be a bit bumpy for awhile. If you're on the borderline with your gear, upgrade what you can and start saving your pennies for a better system if at all possible.