Here are my contributions:
Whether one beleives in a diety or not, its hard to ignore the fact that religion is pretty ubiquitous among us humans. If you count choosing who gets elected President among your goals, then you ignore this fact at your peril.
Many people confuse freedom of religion with freedom from religion and the Republicans of course use this confusion to their advantage.
I've always felt that anyone who thinks the Creator of the Known Universe plays favorites among separate religious practices (let alone political affiliations) is suffering from a supreme failure of imagination.
Stressing that the message of the Democratic Party is one of inclusion should ring true among believer, agnostics and athiests alike. If not, we're just not getting the message across adequately.
Religion is simply politics seasoned with the extra confidence that comes from thinking that the Creator of the Universe has your back.
As such it's very powerful (I happen to think there's a strong genetic component) but at the end of the day, those of us who were taught that God is loving, compassionate and forgiving will believe it to the grave as will all those who think he is vengeful and jealous will do the same.
We'll leave the question of which group votes for which party as an exercise for the reader.
"and the insistence that there is a "natural" explanation for all unexplainable phenomena is no less "faith based" than the belief in God."
I'm not sure if you meant that the way I'm taking it but it's certainly incorrect.
History and experience have shown time and again that the assumption of a natural explanation for all observed phenomena is vindicated regularly and repeatedly. Without such an assumption, we'd still be having difficulties figuring out how to use twigs to harvest termites. Note that you needn't be an athiest in order to insist on natural explanations. The universe is quite sufficiently miraculous on its own without having to postulate uncaused effects.
"a kind of evolving spirituality that is a mix of Buddhism and string theory/quantum physics"
My belief is reasonably easy to state. The Universe should be given at least as much credit for consciousness as it's contents. It is therefore at least as self aware as we are. Like us, I beleive it strives to become more self aware. After that, it's physics all the way down.
"but with what exactly do you disagree when it comes to Jesus' exhortation to lead moral lives and love each other?"
That would be the people who twist the "lead moral lives" part into a reason to hate each other.
"When a woman was brought before Him for her transgressions, Jesus preached mercy, but then told her to go and sin no more."
This is a continuation of the whole "log in your eye vs. a speck in your brother's" message. We humans are imperfect and are not in a position to judge each other let alone invoke God's name when doing so. Those who miss this simple message, as mudcat pointed out in the original post can be reasonably accused of blasphemey Of course the accusation itself would be subject to the exact same logical failure.
In the end the message is clear, that we should be tending to our own transgressions first and formost and leave those of our neighbors in more capable hands.