What Neil Stahl advocates makes perfect sense, and is in concord with the calculus reform projects that I am familiar with. His summary of the algebra required for calculus is incomplete, but as far as it goes it describes perfectly the approach to algebra taken by the Harvard text, for example. I really don't see that we have any big disagreements.
I am puzzled: what is the source of the mistaken belief that the calculus reform movement has advocated not teaching algebra? This is not a rhetorical question; I really would like to know. It would be bad thing if this belief became widespread among high school algebra teachers, for example; if that happened, Neil Stahl's fears could well be realized.