After spending a lot of time on searching in the whole web I decided to report my issue here. It's almost the same like many others I've seen so far.
Main components are : I7-4770, Gigabayte-H87-HD3, Chieftec 500W, Windows 10 PRO
My setup was very stable with RX 480 4GB. I 've bought RX 580 for another computer and put into my PC for testing purposes.
For the first 2 days everything was looking good, but the card started to crash at the booting proces. BSOD says VIDEO_TDR_FAILURE amdkmdag (what a surprise!). The card is not crashing on stress, but just on booting up the whole PC. For the first two days I was able to work and play without any problems.
I did many things proposed on this forum and others. No luck so far. The interesting thing is that if I unistall the drivers with DDU in safe mode eveyrthing is fine, the BSOD appears almost immediately after starting the drivers instalation. I tried 4 diferent versions released this year. Removed some memory modules, checked the BIOS settings. No luck. I didn't do such thing like replacing the PSU or upgrading the BIOS since those are major changes and from what I've seen it didn't help to solve the problem.