I've been seeing this come up rather frequently; The question of how to escape the hardware botnet, or how to escape x86, as a majority of it is pozzed.
Since your question opened with one about single board comupters, you should take a look at this anon >>815608 's link, and look at the 'serious flaws' section, particularly the beagleboard and some of the allwinners, as they are the ones that are Free as in Freedom, minus the GPU acceleration.
Going into your question about other hardware, other than the libreboot thinkpads and macbooks, let's start with desktop computers. I think this is actually the easier one to do and stay modern.
On the libreboot HCL, https://libreboot.org/docs/hardware/ , there are several desktop and server/workstation options. There's a few C2D and Atom options, which are not optimal, but there are a few really nice looking ones.The KCMA-D8, KFSN4-DRE, and the KGPE-D16 are all AMD Opteron boards that can be librebooted, and there is also the new addition of a certain iMac, which is fully compatible apparently, although it does not yet have instructions on the site. As far as getting away from x86, there is also a very nice option here. The TALOS II workstations https://www.raptorcs.com/content/base/products.html are fully Free, and are potentially going to get RYF certified by the FSF soon. They use OpenPOWER, which is an architecture supported by Debian and Fedora (you could probably make Gentoo work too).
Laptops are where shit gets hard. There don't seem to be many options here outside of the Libreboot Thinkpads and Macbooks, and certainly no good ones outside of x86. You'll just have to settle for CD and C2D processors, although there was that rumor of an x220 exploit, and I saw on their notabug that they may be providing support for Core2Quad.
For other options, I think this is less of a "what can I buy right this second" thing, and more of a "what can I look forward to" thing. There does appear to be a Libre ARM laptop with EOMA68 https://www.crowdsupply.com/eoma68/micro-desktop , but have fun using 1.2GHz and 2GB of RAM. At that point, you might as well be using one of those SBC pcs as your laptop, which is kinda what this is. Same goes for the pinebook https://www.pine64.org/?page_id=3707 it looks nice, but once again it's literally a shitty SBC in a laptop, and in this case, I don't think it's even Libre. Purism looks like something to keep an eye on. While they are not Libre, and thus far only have coreboot and """apparently""" a removal of the ME, they do appear to want to go a step further. A very overlooked page on their site is this one https://puri.sm/learn/freedom-roadmap/ which outlines their goal of going all the way to 100% freedom, and where they are on that road to it.
In any case, RISC-V looks like something else to look forward to. Hopefully someone makes a fully usable computer with it that runs on Free Software, because right now it looks quite promising.