*edit*
Ok, I found out my basic mistake with the functions.php, i.e. that the child theme functions.php does not replace but supplement the parent theme function file.
I also found some tutorials/documentation in the web, how to remove functions (remove_theme_support, etc., for example here: https://wp.tutsplus.com/tutorials/creative-coding/how-to-modify-the-parent-theme-behavior-within-the-child-theme/), but none of the examples showed there seem to work with the way it is set up in Fluxipress, as the customisation code for the theme looks very different (to me anyway) in the functions file.
