Is there any way to fix... this issue?

Is that a no, then?

Yeah, I'm not liking this either. It's difficult if you are a healer to see through the buffs/debuffs.

There are some buff options in the settings, if you turn on onlyshow player that will resolve the issue. There will be more option in 6.0

There is no option for only displaying player buffs, I already went looking for such an option. Perhaps I am truly blind and cannot see it?

nope guess it is missing from party options. Another case of the pre-6.0 frame being horibly fragmented and leading to poor customization.

Try one of the other skins for party frames like war or fel.