While I agree and have no problem with furries, I think the issue is people seeing, what a lot of people in their own community see as linked to a sexual kink, being brought out into public spaces.

"Sexual attraction to furry characters is a polarizing issue. In one survey with 4,300 furry respondents, 37% answered that sexual attraction is important in their furry activities, 38% were ambivalent, and 24% answered that it has little or nothing to do with their furry activities."

"Another survey at a furry convention in 2013 found that 96.3% of male furry respondents reported viewing furry pornography, compared with 78.3% of female; males estimated 50.9% of all furry art they view is pornographic, compared with 30.7% of females."

Source: https://en.m.wikipedia.org/wiki/Furry_fandom

So like clearly there is a large sexual component to the fandom, and I think it weirds people out and makes people uncomfortable when they see these people wearing their fur suits out in public. Which again to be clear is not something the entire community does or even tolerates, but there's enough people who do so that it's become part of the cultural zeitgeist.

But it's also just the fact that it's so far from normal vanilla experiences. Everyday people think role playing sexually is already adventurous and out there. Now add big animal suits that are typically associated with mascots for entertaining children and I think anyone can see why everyday people think it's weird.