NTR is pretty much avoidable, my first playthrough was pretty much a harem game. There are some requirements though and at least a few minor side characters that I don't think are avoidable. Off the top of my head you need high/max luck before doing Rin's shower scene or else Rei catches you and starts being okay with cheating. You also need to accept the redhead becoming your girlfriend which iirc has requirements.
Characters you probably can't avoid some level of NTR for include emily the dark hair prostitute lady. If you advance her relationship and pay her debt you can tell her to stop working as a prostitute though. There's also the A class teacher who's getting fucked by Souta and the school nurse who's getting railed by students and the principal (the principal scenes are genuinely disgusting). There's also the two C class gyaru students. At least one of them actively works in the strip club as a weekend dancer and both are easy to see fucked by the principal. I believe you can convince them to stop seeing the principal if you raise their affection before his gets too high. There's also the PE teacher who can fuck the athletic student if she loses enough races. You can make sure this never happens by avoiding letting her challenge him.
All that said, 70% of the content is centred around the house girls and you can avoid NTR with them. It's also possible to get most of the rest to stop NTR content.
You can go once a week from the west central area through the subway train. The train drops you in a separate city that has a hot spring and a shrine. The shrine gives you 1 luck when you donate, though I think it's limited to once a week to actually get it while you can just continuously donate for no reason.
