Some further tests:
=> Dell P2415Qb with two different cable @ RX 590 DP => blackouts
=> Dell P2415Qb with two different cable @ RX 590 HDMI (only 30 Hz) => no blackouts
=> Dell P2415Qb @ R7 250 PD => no blackouts
=> Dell U2515b with two different cable PD@ RX 590 => no blackouts
Could it be, that the RX 590 with DisplayPort 1.4 causes trouble and the R7 250 with DP 1.2 doesn't? Any way to set the RX 590 to DP 1.2?