This is an interesting discussion, and Ted and I touched on it the other day while chatting. I find when I'm talking with my fellow non-religious friends or acquaintances that they totally get *secular* Buddhism because they understand the word secular. Sometimes they will ask how secular Buddhism works, as opposed to traditional, what the differences are, etc. But most atheists understand the word secular to mean non-religious.
I find the confusion or resistance comes when I'm speaking with either Christians or traditional Buddhists. Their reactions are similar. The Christians can be put off by both the terms secular and Buddhism, or one or the other. But I encourage discussion with them, as I find they have misconceptions. Generally their problem is my lack of belief in their god concept.
Traditional Buddhists have actually been the people who react with the most hostility towards me. This was surprising because I had the erroneous stereotype of Buddhists as people being open to new ideas, to change, and to a practice that includes what they're doing: meditation, mindfulness, ethics and morality, compassion, etc. And I just leave out the "beliefs" in things for which there isn't compelling evidence and that I can't test in my practice.
I have been told I will be reborn in many hells (that's not new, as I've been told that from my Christian background, but it was one hell, now many) and I was told that I am sending everyone I talk to about this to many hells. I don't recall Buddha ever saying that people's words would send others to hell realms.
Anyway, point being, when I'm asked what secular Buddhism is, I explain what I can. I always make a point not to call myself a Buddhist, but to say I practice secular Buddhism, because it helps me focus on the practice and not fall into dogma. I'm not saying you shouldn't. And I agree with Mark that secular Buddhism is not and must not become a religion. I know we disagree with Stephen Batchelor on this point, as Stephen feels secular Buddhism is a religion. While technically his definitions may be sound, the connotation, at least in the US of religion, means a belief in god or metaphysics. I share no beliefs in those, and do NOT consider myself religious.
So, in short to answer the original question, I do not claim to be both secular and religion. I claim only to be secular and to practice Buddhism through mindfulness meditation, ethics, and compassion.