I'm having issues also - I have 2 new LG 4K screens and 1 old crap Dell that I rotate and use for long lists (for example) that don't change much.
NONE of the 3 displays worked. It seemed that nothing I did would change anything and I was pulling my hair out! And no, it's not FileVault; there are too many inconsistencies in the reports, and there are too many having trouble who don't use FileVault at all. But guys - the answer is not to immediately throw tomatoes at Apple, say that they suck, it's all their fault, that quality control is down, take it back to the store, yell at people on the phone, etc. Please, put your torches and pitchforks away for a moment.
I needed to have some patience. Like some of you I stripped it down and started with one display at a time, with just the Mini (I had also bought the BlackMagic eGPU). What you need to do next is not to add a second, and then the third; it's to do one display again - a different one. Use the same cables you used for the first display, if you got that one working. Then the third one by itself. Doing this I discovered that each of my screens worked just fine with my new Mini. And I also learned that those particular cables were good. Now I was feeling a bit relieved, because I was beginning to think that I had made a mistake in buying everything that I did.
Looking at Apple's instructions, it seems that the best way to attach my particular displays is via DisplayPort for the 4K screens, and HDMI for the crappy Dell. And so I connected the Dell - with a DVI to HDMI adapter - to the Mini and got...nothing. No worries - no need to reboot, reinstall, zap the VRAM, etc. I just messed with the cable and the adapter a bit and lo and behold, a picture appeared! It would seem that I might have a bad cable. Now I'd add in more - the eGPU, with a thunderbolt cable. Tried to use the HDMI port there instead of the Mini. Also tried the second display by DisplayPort to thunderbolt on there. No joy. Sure, I was frustrated...but not yet time to develop a hate-on for Apple. I looked around and found the thunderbolt cable that came with the GPU (I was using another cable instead because it was longer). Replaced the cable - and both screens now worked.
I still haven't got the third display up and running...but I'm sure I will. I don't have a signal, but I have power to it now - because it needed to be moved from one outlet to another in the UPS (sheesh!). And I'm not saying that there isn't an issue - I believe there is something strange going on. But I also believe too many were too quick to jump on the "They Suck! Kill Apple!" bandwagon. Spend a little time with your Mini, guys - make sure there aren't any bad cables, adapters, outlets, or configurations. Maybe some patient troubleshooting will help a few of you? I hope so. Good luck with everything.