Qt5 is not broken on freshly installed Antergos Mate 1.18.
Run Qt5 Configuration Tool qt5ct from the command line:
You’ll see in terminal
qt5ct: using qt5ct plugin
Configuration path: /home/just/.config/qt5ct/
Shared QSS path: /usr/share/qt5ct/qss/
And Qt5 Config window will open:
Set Qt5 as you wish. Close the config window.
QT_GPA_PLATFORMTHEME env var doesn’t exist. Instead, QT_QPA_PLATFORMTHEME does exist and is set by qt5ct:
└─> echo $QT_QPA_PLATFORMTHEME
Once Qt5 was configured from the command line, Mate’s Control Center --> Look and Feel --> Qt5 Settings may be clicked. With about 2 seconds delay the Qt5 Configuration Tool window will be opened.
Nihil sub sole novum. Everything is already described in ArchWiki. Qt5 under DEs different from KDE Plasma is explained here.