I've been using my 5700XT for about a month now in an older PCI-E 3.0/AM3 system running Windows 10 on an FX-6300 processor. Everything was just fine. My R9 3900X finally came in after a month of waiting, and I put my new system together.
The result? Constant BSODs and crashes when browsing the internet. I finally narrowed it down to video content within Firefox (68.0.2) causing it. I disabled all hardware acceleration in Firefox, and my system has not BSOD'd since, when before it'd pretty reliably BSOD if I opened enough tabs with video content. Sometimes if someone sends me a video through steam, Steam Friends will crash and then reload with hardware decode disabled.
Playing video content through VLC does not seem to cause any issues (maybe It's VP9 decode?). I've also had some issues with the game MudRunner crashing, but I didn't have that game with the old system so I can't say if it's just the game or something else. No other game I've tried seems to have issues.
I also have severe bugs with refresh rates and my Pixio PX275h monitors. With both monitors enabled, the video memory is stuck at 875MHz. With one monitor enabled, only 60Hz works correctly. 75Hz is completely bugged and unustable, and the system will basically eventually crash. WattMan doesn't even function correctly at 75Hz. A single monitor enabled at 95Hz (monitor maximum) seems to work okay, but memory is once again stuck at 875Mhz like it is with dual monitors.
I don't know if it's PCI-E 4.0 causing these errors or what. I do have one WHEA error on every boot up, and that's with the latest 184.108.40.206ABB AGESA. I'm using an R9 3900x, ASUS TUF x570 WIFI, XFX Reference 5700 XT, 16GB GSKILL 3200 MHz RAM, Seasonic Titanium 750W PSU and a Samsung 970 EVO 1TB connected to the first M.2 slot. Using fresh install of Windows 10. It's not the RAM - it passed 3-4 hours of Memtest86. I've tried running it at both 2400 and 3200 MHz speeds with the same results.
Disabling hardware acceleration in Firefox stopped the BSODs. Most of the BSODs were IRQ_NOT_LESS_OR_EQUAL, or SYSTEM_SERVICE_EXCEPTION. I did have one crash that was a straight up reboot, no BSOD or anything.