This game is actually great. The developer has generally made it quite clear that there won't be any NTR content after consistent backlash, and don't worry, there isn't in game currently.
I think by "consequences" for neglecting choices, they mean that potential love interests could die.
This is a Time travel isekai after all, so the main character actually has knowledge of these girl's potential fates, and basically none of them are NTR related.