Here it is, 2020 and we're still having this issue! I too have no video output from a RPi 2 model B using an Acer S200HQL monitor. It appears to be booting (red and green led activity) but i'm using a wifi usb dongle which cannot be configured without a monitor, so i haven't tried to SSH into it. Put another SD card in and it works fine. Something not right with Ubuntu-MATE 18.04!
Also, FYI--Using Raspian with the EXACT same stuff (including SD card) I have no problems. Monitor displays boot up sequence, even showing the rainbow square in the beginning. Come to think of it, that's odd that the square doesn't show up with Ubuntu, since i thought that square was a hardware thing, not an OS (SD card content) thing. So my only guess is, that Ubuntu is very quickly disabling the video output for the Acer monitor for some reason. Maybe a bad handshake with the HDMI.