In all honesty, yes, being a fur is a strange thing. It is a little weird but that's why furs love it. Because it makes them happy. There are some people who do it just for the fun, others are furry for a hobby, and a few whose lifestyle is entirely furry. As one of my fur friends once said "people don't see how just wearing a costume can prevent someone from self harm or alcohol abuse. I mean, those are hobbies too." 

Some people come into the furry fandom with nothing but anxiety and animal drawings, but when they're around people with common interests they can turn into a social butterfly right before your eyes. This hobby isn't hurting anyone so why is it rejected by people?

(I do NOT promote any of the following listed.) Smoking can help people calm their nerves. Alcohol can provide someone with liquid confidence. Self harm can help with emotional stress. So why can't people just perform an activity that's harmless to themselves and others?

Yes, a fair portion of the fandom is LGBT but there is also a good lot who are straight. The furry community is rather welcoming and lets anyone join since there is no initiation or process to go through to join. And since some people want a place to escape, they can happily do so through colorful animal drawings. Let's suppose there was a queer teenager who hadn't told their parents about their orientation. They might not want to tell the parents because maybe they're strict Christians or the parents may disown the teen for it. This teen stumbles upon the furry fandom where they buy a fursuit and can be a gay pink husky if they so please. They can go to conventions and flaunt whatever they want and not fear being judged since they're just a giant pink dog. You see what I'm saying? It's like a reversal to the comic "on the internet, nobody knows you're a dog". 

Often through drawing their fursona or wearing a fursuit, LGBT community members can express themselves. Since (please correct me if I''m wrong) each color in the pride flag stand for something, they can make a character with their corresponding traits as shown by the flag (ie. green is nature, turquoise is art, yellow is sunlight, blue is peace). This allows them to show what they are and how they feel but remain anonymous to others.