Non-binary people shouldn't be part of the transgendered community, or at least I don't think of them as part of it.
Why don't you consider non-binary people part of the transgender community?
Because they make others feel uncomfortable about their gender choice and as non-binary, they are not making and actual gender choice.
I know you feel uncomfortable with non-binary people, but it's not right to judge and entire group of people. Non-Binary people have the right to include themselves with whatever group they prefer. They are judged by many people and are likely very sensitive to the judgements of others.
It doesn't matter to me, I don't consider them as part of the community.
You will be considered the bad person here if you continue with this line of thought. You should be accepting of people, no matter how they are. Someone who is in the LGBT+ community of all people should respect not judging others.