Memes aside, I'd keep it to private events, not walking in public with a fursuit. Fetishes are not really a thing you want shared with everyone you met
Seeing them at conventions or other event setting would not really be that odd. Seeing one just out and about wearing a suit doing everyday things would be weird. I wouldn't think it would be comfortable to go about it and drawing that much public attention to oneself just seem awful.
It's weird to me, but I don't care so long as it's not negatively impacting other people. I personally wouldn't want that kind of attention drawn to me.
My only interactions thus far with Furries have been somewhat disconcerting. There was a fella I knew for some time who was always a little "off" if you will. Than to my surprise one day me and some of my friends who also knew him ran into him in public with his new girlfriend that they apparently knew. He had convinced her to shave her head and she just started openly telling the girls among us that it was a kink of his, the shaved head and diaper thing, pretending to be a baby and such. He also whole heartedly believed himself some form of reincarnated furry from some other dimension or such... I kinda stopped talking to him, I mean I can neither prove nor disprove his being some sort of reincarted furry royalty, but I also could no longer look at him without the vivid details his girlfriend told us about his fetish appearing in my head... or wonder if he was wearing a diaper at that very moment.
I've met furries at conventions. And, speaking as someone who saw Lola Bunny and Renamon when I was young, I never had a chance. I don't have a fursuit, but if I could fuck Lola or Renamon, I absolutely would.