Depending on the options you choose during the judgments, some party members will approve or disapprove (just like when you're making larger decisions in game). In most cases, it's not a big loss unless you do something severe that a party member would absolutely hate (like being able to make Alexius tranquil which Solas really dislikes)
Some judgments are there for entertainment (like the Avvar chieftan)
Some judgements can get you an agent depending on your choice (like the Duchess in a box)
Some judgements get you additional war table missions (like conscripting Servis)
Some judgements will get you items (like giving Samson to Dagna so she can research him)
Also, with the party members who can leave, you would have had to made multiple decisions that they severely disliked in order for them to leave. If you're worried about a party member's approval from your decision, save before you do the judgement, make your decisions, and see who likes/dislikes your choices.
