I don't really understand why, in Forbidden Scrollery, Reimu tried to not point out who Mamizou is. I mean, it states that it would ruin her reputation with the human village but wouldn't it be more logical to come to the conclusion with that Reimu fought/exterminated her before. Instead of thinking that Reimu became friends with Mamizou or something.
Basically, what I'm trying to say is that, I'm confused over why the villagers would lower Reimu's reputation over knowing Mamizou.
The villagers don't really know Reimu, they just know rumors about her, since Reimu does not visit the village that often.
Reimu's reputation with the village isn't exactly good either. While she is a youkai hunter, she is not strict enough on youkai. Her shrine is sometimes known as a youkai shrine, because youkai visit her, again causing a reputation drop.
Real youkai hunter, like way back when, hunt down and exterminate youkai without exception. Byakuren was sealed because she was friendly with youkai back in the day.
The logical conclusion to draw from someone you don't really know and they are hanging out with youkai is that the person is on friendly terms with that youkai.