I'm sorry but the only way I can describe that perspective is "delusional". First of all, I'm going to point out that by starting your conclusion with "All furry hate", you've already revealed that you're simply here to make generalizations instead of to be accurate. Nearly no statement that starts with "all", "none", "every", etc. about such a large group (furry haters) is even worth considering.

Now that I've gotten that out of the way: No, people don't hate furries because they're LGBT. Most people know nothing about the movement or its founders, and don't care to. People dislike the furry community because:

1. Fursuits look weird. Mascots and the easter bunny fall into this category too. Non-fursuit anthropomorphic animals (eg. Looney Tunes) are generally well-regarded, even somewhat if they're from the furry community.

2. Someone told them about yiff or showed them a vore picture and now they hate all furries.

3. Their primary interactions with furries lead them into direct contact with "the weird kids" aka assorted cringy 12 year olds. Any community with a significant number of preteens will have this same repulsive effect on older teenagers and young adults, or even other preteens. See also: Fortnite, Skibidi Toilet, FNAF to some extent, Roblox, etc.

That's it. There's no grand anti-lgbt conspiracy. Furries are just weird. If you want, I have access to a discord server that's like 60-70% queer and I can make a google form to prove this.