I wished I had libreboot!
Yes: Full-disk encryption. It never gets to the password prompt. This is all I get:
AMD-Vi: Unable to write to IOMMU perf counter
starting version 238

It boots with linux-libre-lts. I think that it stopped working near 4.15 (possibly one or two updates before). It definitely is there with the latest kernels. As a matter of experience, I keep the lts kernel installed and old kernels in the pacman/pkg directory. Linux-libre-xtreme has the same issues.

$ lscpu 
Architecture:        x86_64
CPU op-mode(s):      32-bit, 64-bit
Byte Order:          Little Endian
CPU(s):              8
On-line CPU(s) list: 0-7
Thread(s) per core:  2
Core(s) per socket:  4
Socket(s):           1
NUMA node(s):        1
Vendor ID:           AuthenticAMD
CPU family:          23
Model:               17
Model name:          AMD Ryzen 5 2500U with Radeon Vega Mobile Gfx
Stepping:            0
CPU MHz:             1586.199
CPU max MHz:         2000.0000
CPU min MHz:         1600.0000
BogoMIPS:            3992.26
Virtualization:      AMD-V
L1d cache:           32K
L1i cache:           64K
L2 cache:            512K
L3 cache:            4096K
NUMA node0 CPU(s):   0-7
Flags:               fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx mmxext fxsr_opt pdpe1gb rdtscp lm constant_tsc rep_good nopl nonstop_tsc cpuid extd_apicid aperfmperf pni pclmulqdq monitor ssse3 fma cx16 sse4_1 sse4_2 movbe popcnt aes xsave avx f16c rdrand lahf_lm cmp_legacy svm extapic cr8_legacy abm sse4a misalignsse 3dnowprefetch osvw skinit wdt tce topoext perfctr_core perfctr_nb bpext perfctr_llc mwaitx hw_pstate sme vmmcall fsgsbase bmi1 avx2 smep bmi2 rdseed adx smap clflushopt sha_ni xsaveopt xsavec xgetbv1 xsaves clzero irperf xsaveerptr arat npt lbrv svm_lock nrip_save tsc_scale vmcb_clean flushbyasid decodeassists pausefilter pfthreshold avic v_vmsave_vmload vgif overflow_recov succor smca

$ uname -r
4.14.34-gnu-1-lts

I don't know if this is good news, but I did a fresh install with the complete install liveiso (Linux parabolaiso 4.13.11-gnu-1 #1 SMP PREEMPT Fri Nov 3 21:09:48 CET 2017 x86_64 GNU/Linux), and the computer boots and reboots correctly. I don't dare to say exactly which file I used for the iso, but it could be this: parabola-systemd-cli-dual-complete-2017.10.17-21.39-alpha.iso. If you let me know how I can check that, I can report it correctly.

So, the issue arises between 4.13.11-gnu-1 and 4.15xx. Is it just the kernel? I don't know (may be linux-libre-firmware?).

If you are sure it's a kernel issue, please show us your whole dmesg output, the one of the working kernel and the one of the non-functional one (if possible).

After long time of having crashed my computer, reformatting, re-encrypting, etc. I can confirm that the issue is the kernel. I upgrade the whole system ignoring the linux-libre package. Once I upgrade the kernel, the booting process stops working. The linux-libre-lts 4.14.48-gnu-1-lts works, but does not shutdown nor reboot. There is no problem with the fresh install: linux-libre 4.13.11-gnu-1.

Let me know if there is anything else that I can provide (and why is this marked as info needed?)

Good news! My system boots, shuts down and I have a graphical interface (https://labs.parabola.nu/issues/1685, https://labs.parabola.nu/issues/1819#note-18). This is what I did (from the first link):

- Update the system

# optional: rm -fr /var/lib/pacman/db.lck
pacman -Rnucs libxfont
pacman -S libxfont2
pacman -Sy parabola-keyring archlinux-keyring
pacman-key --refresh-keys
pacman -Syu --noconfirm

- Get rid of-- and reinstall lightdm

# Manually CTRL + ALT + F2 to login into a virtual console (login with your credentials)
systemctl stop lightdm
ps aux | grep lightdm  # get any running instance
top  # just to make sure that it's not hanging around
kill -30 <any lightdm related process>
pacman -Rnucs lightdm lightdm-gtk-greeter lightdm-gtk-greeter-settings
pacman -U /var/cache/pacman/pkg/linux-libre-4.17.2*  # reinstall any kernel you want (just to make sure)
pacman -S lightdm lightdm-gtk-greeter lightdm-gtk-greeter-settings efibootmgr

- Reinstall the bootloader

grub-install --target=x86_64-efi --efi-directory=/boot/efi --recheck  # --boot-directory=/boot automatically; the --bootloader-id=parabola
grub-mkconfig -o /boot/grub/grub.cfg

- Reboot

Solved! https://labs.parabola.nu/issues/1685#note-7

I nailed it down to this:
amdgpu is breaking my installation. If I remove amdgpu from mkinitcpio.conf (MODULES) and run pacman -Rnucs xf86-video-amdgpu, I can boot and shutdown

AMDGPU definitely interferes with the booting process. One can input the password after the blank screen (blindly, without knowing what is going on; after a bit of time) if amdgpu is enabled in mkinitcpio.conf with MODULES=(... amdgpu ...)

pacman -S mesa libva-mesa-driver libva-vdpau-driver mesa-vdpau libvdpau-va-gl libva libva-utils vdpauinfo xf86-video-amdgpu
mkinitcpio -p linux-libre  # change linux-libre for your version or use -P instead

I am going to shutdown and restart to see if that is affected.

Restarting goes well (not tested with other kernels).

$ uname -r
4.17.3-gnu-1

$ lspci | grep -i vga
03:00.0 VGA compatible controller: Advanced Micro Devices, Inc. [AMD/ATI] Raven Ridge [Radeon Vega Series / Radeon Vega Mobile Series] (rev c4)