I'm having difficulty finding the time I want to respond to this, so I'll do a quick post now with my main points in no particular order and maybe a more thourough one next weekend.
I'm a confirmed agnostic and I like being a member of the Brights movement. I'm active on their discussion forums and I do not feel that I'm out of place because I'm not an atheist. Its not just a group of atheists. I believe I saw a poll in the Brights forums and of the less than 100 people that responded, the atheists and agnostics were close to evenly split. This is one of the things I'll try and verify when I have more time.
The point of the movement is not to help agnostics and atheists and humanists etc come to agreement on our beliefs. It is to help us to work together in recognition of the fact that we all have common needs and in recognition of the fact that the differences between us are trivial when it comes to matters of our everyday lives. In fact the definition is intentionally vague because the movement doesn't want to limit our numbers because of the details of what we think supernatural means (or waste time debating the meaning). If I say my worldview is free of supernatural elements (and my definition of the word is somewhere in the realm of reasonal definitions) than I could be a bright.
In my mind, if somebody can prove something then its not supernatural anymore. It can still be unexplained, but the fact that its proven to exist takes it out of the realm of the supernatural. I'm sure that many of the atheists in the Brights movement would probably agree with me on this point.
I like having the option to use the term Bright, but the movement doesn't require that I ever call myself a Bright. I like it because going around calling myself a word that is derived from a concept I find unlikely seems silly. It is often compared to the idea of calling myself an agsantaist because I can't prove santa doesn't exist. It gives too much credibility to the idea of santa and it makes it sound like I don't like him instead of like I think he's a myth. I also sometimes use it when I know that the person I'm talking to will interpret me saying "I'm an agnostic" as "I'm confused" and I won't get the chance to correct it. At least for now, they'll have to ask me what I mean. Someday, they'll supply their own erroneous definition such as "a bunch of atheists looking to update their image with a flowery new-age name"
The Brights movement seeks equality with Supers. It is not anti-religious. It is a tool to help us stand up for our rights. There are however Brights who could be considered anti-religious and you would see that very clearly on their discussion forums. However, the movement itself and many of its members are not anti-religious. For many of us, especially those of us married to Supers this is one of the positive attributes of the Brights Movement.
The movement discourages the use of the term Bright as an adjective for the sole reason that we don't want people to think we mean it as an adjective. It is a noun. We try not to say "I'm Bright". Instead we say "I'm a Bright". The movement intentionally chose a positive sounding word for Supers to further try and offset the perception caused by the name. When I first learned about the Brights I thought that the name was a poor choice and I ignored the movement for about a year. Then it popped up on my radar again and I gave it a second look and realized I liked what they were up to and recognize that every name has some drawbacks.
One of the big rules of the Brights Movement is that we do not speak for each other without specific permission. So, anything I've said above that sounds like I'm telling you what other Brights think is just my guess at what they are thinking.