  Let $A$ be a homogeneous C*-algebra and $\phi$ a state on $A.$ We show that
if $\phi$ satisfies a certain faithfulness condition, then there is a net of
finite-rank, unital completely positive, $\phi$-preserving maps on $A$ that
tend to the identity pointwise. This combined with results of Ricard and Xu
show that the reduced free product of homogeneous C*-algebras with respect to
these states have the completely contractive approximation property. We also
give an example of a faithful state on $M_2\otimes C[0,1]$ for which no such
state-preserving approximation of the identity map exists, thus answering a
question of Ricard and Xu.
