To be fair, the community doesn't always show itself in the best light.
What probably 'shines' through the most is the immature (and oftentimes cringeworthy) behavior, and loads of ... um, unconventional porn. Nothing sells a community quite like seeing Sonic characters getting inflated and vored (sorry to anyone who's actually into that)
I think it can be narrowed down to three main factors:
People in the furry fandom tend to be much more open and positive with their feelings and expression, to a degree that feels comical to the average onlooker, and makes them uncomfortable like a second-hand embarrassment. Some people take the as an offense to their dignity I suppose.
Furries are a very diverse subject, so there are going to be designs in the fandom that, to outsiders, might seem uncanny or strange to them.
- Sexuality (Cw)
A lot of kinks and subcultures make their way into the fandom and kinda develop their own genres, but unfortunately in some cases people do nasty things which makes rounds through the internet, and be misinterpreted as a representation of the fandom. While abhorrent behavior like bestiality or pedophilia is not acceptable, it isn't uniquely inherent to the fandom, and more a symptom of the medium of internet cultures as a whole.
A lot of youtubers and influencers who cover r/creepyasterisk find furry content in there. The asterisk (*) was used for RP a lot, and many in the furry community would just initiate NSFW RP with strangers who didn't ask for it, hence getting screenshotted and shared on Reddit.
I still see the occasional "furry gas chamber" pictures or the "1 like/repost = 1 dead furry" or the varying con-shooting memes and all that.
I think furries are targeted for being different and are largely only accepted by each other. And of course, things like fursuits and the sexual aspects of any subculture are always going to be unpopular with out-groups.
I thought the FlashGitz videos were hilarious, personally, because of their over-the-top absurdism.
Increasingly, it's seeming like furry haters these days are mostly middle schoolers desperately trying to be edgy and cool; old goons who haven't gotten the memo that it's not 2009 anymore; and Karens, prudes, bigots, and curmudgeons who basically hate everything.
We're "weird" so people will now look everywhere for every shred of "evidence that all furries are bad" (such as the small minority of zoophiles and people who don't respect boundaries) to justify them hating us, or just straight up admit they dislike us solely because we like something that they don't. It's the same reason people hate people who like anime, certain video games, and more serious communities like gay and trans people.