Let's consider the setting of this manga first. This is a Victorian era with a mix of fantasy where human nobles already have fiances at a young age so it's taboo and utterly wrong for the little sister to share a bed with 3 different men who have fiances especially when one of those said men is literally the crown prince aka ex-fiance of our MC. You mentioned poly but poly relationships have people know each other and gave their consent if they want to share someone / or be in a poly relationship but in this case, the crown prince was shocked to find out then and there that the little sister bedded his own two aides so therefore, this is under 'cheating' or 'triple-timing'.
Honestly, based on every dragonoids in different mangas that I've read, they all have sensitive sense smell so if he can smell three people on the little sister then that means she recently or done multiple times in the sheets with these men for it to be overwhelmingly smelly and cause a great shock to this guy. So I guess this is karma for the little sister for touching someone who isn't hers to begin with.
I'm going to say 2 things of why he gave a shit with the horny ape since Alenira has explained about why the dragon called her ass out for being the OTHER WOMEN of those jerks
1. That honry ape made a move first to the dragon, which, is a crown prince of another nation. It is inherently rude to be speaking without their permission.
2. That ape also insulted his soon-to-be mate publicly after, the audacity of stealing her SISTER's 'fiance'. Imo he is completely justified to say that, though.
Eh he didnt slut shame, all he did was question if it was common for Human women to have multiple men while engaged, becaus his race has one mate and one mate only. It was his first time interacting with the human kingdome. So he wanted to know if it was normal and ment no harm, because to him it seemed abnormal. Hench he asked after she flirted with him to state his stance.

why do we gotta slut-shame.. humans are freaky lil bipeds who fuck for FUN.. let alone the countless species who are promiscuous (most common breeding pattern). like BRO, poly relationships EXIST yet get shit on HEAVILY by most genres (or fetishized).
you would thing a dragon, who is often associated with nature and the “natural order” wouldn’t be such a PRUDE